One of the criteria for lines being perpendicular is the fact that the slope of the function in a perpendicular line is the inverse of the slope of the first times -1.
And as you can see m (being the slope of the first equation) is the inverse of the second equiation:
[tex]m=\frac{7}{3},m_1=-\frac{1}{m}[/tex][tex]-\frac{1}{m}=-\frac{1}{\frac{7}{3}}=-\frac{3}{7}[/tex]Therefore line 1 is perpendicular to line 2.
Rectangle R measures 18 in by 6 in. Rectangle S is a scaled copy of Rectangle R. Select all of themeasurement pairs that could be the dimensions of Rectangle S.24 in by 8 in9 in by 3 in2 in by 1 in6 in by 2 in3 in by 2 in
In order to find possible dimensions for the scaled rectangle, the proportion between the dimensions of the rectangles must be the same.
So first let's find this proportion for rectangle R:
[tex]\frac{18}{6}=3[/tex]Now, let's find the proportion of the possible options of rectangle S:
[tex]\begin{gathered} \frac{24}{8}=3 \\ \\ \frac{9}{3}=3 \\ \\ \frac{2}{1}=2 \\ \\ \frac{6}{2}=3 \\ \\ \frac{3}{2}=1.5 \end{gathered}[/tex]So the correct options are the first, second and fourth options.
Downhill RacerA snowboardertravels 105 metersin 7 seconds.A skier travels for4 seconds andcovers 72 metersHow far will a skier travel in 2minutes? Explain how you figured it out.
To be able to determine the distance that the skier travels, let's first determine its constant rate (speed).
A skier travels for 4 seconds and covers 72 meters.
Constant Rate (Speed):
[tex]\text{ }\frac{\text{ Distance Traveled}}{\text{ Time}}\text{ = }\frac{\text{ 72 meters}}{\text{ 4 seconds}}\text{ = }18\text{ meters/second}[/tex]Determining the distance covered in 2 minutes:
Step 1: Convert the time in minutes into seconds.
[tex]\text{ 2 (minutes) x }\frac{\text{ 60 seconds}}{\text{ 1 (minute)}}\text{ = 2 x 60 seconds = 120 seconds}[/tex]Step 2: Multiply the time by the constant rate (speed) of the skier.
[tex]\text{ Distance Traveled = 120 (seconds) x }18\text{ }\frac{\text{ meters}}{\text{ (second)}}[/tex][tex]\text{ = 120 x 18 meters}[/tex][tex]\text{ Distance Traveled = 2,160 meters}[/tex]Therefore, in 2 minutes, the skier travels 2,160 meters.
Can someone help with this question?✨
The equation of the line that is perpendicular with y = 4 · x - 3 and passes through the point (- 12, 7) is y = - (1 / 4) · x + 4.
How to derive the equation of a line
In this problem we find the case of a line that is perpendicular to another line and that passes through a given point. The equation of the line in slope-intercept form is described below:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.In accordance with analytical geometry, the relationship between the two slopes of the lines are:
m · m' = - 1
Where:
m - Slope of the first line.m' - Slope of the perpendicular line.If we know that m = 4 and (x, y) = (- 12, 7), then the equation of the perpendicular line is:
m' = - 1 / 4
b = 7 - (- 1 / 4) · (- 12)
b = 7 + (1 / 4) · (- 12)
b = 7 - 3
b = 4
And the equation of the line is y = - (1 / 4) · x + 4.
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What is the slope of the line in the graph?A. 1 B. 2C. 0 D. -2
Always remember that the slope is the number of units on the Y-axis in relation to the X movement.
A horizontal line always has a slope of 0. (it is not increasing in the Y-axis)
Can someone help me with this math question. I just need to see the work.
pic of question below
The polar coordinates for each point are given as follows:
a. [tex](r, \theta) = \left(2\sqrt{5}, \frac{7\pi}{4}\right)[/tex]
b. [tex](r, \theta) = \left(6, \frac{\pi}{3}\right)[/tex]
Polar coordinatesSuppose we have a point with Cartesian coordinates given as follows:
(x,y).
The polar coordinates will be found as follows:
r² = x² + y².θ = arctan(y/x).For item a), the Cartesian coordinates are as follows:
(-4, 4).
Hence the polar coordinates will be given as follows:
r² = (-4)² + (4)² -:> r = sqrt(32) = 2sqrt(5).θ = arctan(-4/4) = arctan(-1) = -45º = 2pi - pi/4 = 7pi/4.For item a), the Cartesian coordinates are as follows:
(3, 3sqrt(3)).
Hence the polar coordinates will be given as follows:
r² = (3)² + (3sqrt(3))² = 9 + 27 = 36 -> r = sqrt(36) = 6.θ = arctan(3sqrt(3)/3) = arctan(sqrt(3)) = 60º = pi/3.More can be learned about polar coordinates at https://brainly.com/question/7009095
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Sean, Kevin and Bill take classes at both JJC and CSU. Sean takes 8 credits at JJC and 4 credits at CSU; Kevin takes 10 credits at JJC and 6 at CSU: Bill takes 6 credits at JJC and 4 at CSU; the cost per credit at JJC is $103 and at CSU is $249. a) Write a matrix A that gives the credits each student is taking and B that gives the cost per credit at each school. b) Find the dimension of A and B. c) Find the product AB and the names of its rows and columns.
ANSWER:
a)
[tex]\begin{gathered} A=\begin{pmatrix}8 & 4 \\ 10 & 6 \\ 6 & 4\end{pmatrix} \\ B=\begin{pmatrix}103 \\ 249\end{pmatrix} \end{gathered}[/tex]b)
Dimension A = 3 x 2
Dimension B = 2 x 1
c)
Cost of credits
Sean $1820
Kevin $2524
Bill $1614
[tex]\begin{pmatrix}Sean \\ \: Kevin \\ \: Bill\end{pmatrix}\begin{pmatrix}1820 \\ \: 2524 \\ \: 1614\end{pmatrix}[/tex]STEP-BY-STEP EXPLANATION:
With the help of the statement, we create the matrices A and B:
[tex]\begin{gathered} A=\begin{pmatrix}8 & 4 \\ 10 & 6 \\ 6 & 4\end{pmatrix}\rightarrow3\times2 \\ B=\begin{pmatrix}103 \\ 249\end{pmatrix}\rightarrow2\times1 \end{gathered}[/tex]Now, we calculate the product just like this:
[tex]\begin{gathered} \text{Product }A\cdot B=\begin{pmatrix}8\cdot103+4\cdot249 \\ 10\cdot103+6\cdot249 \\ 6\cdot103+4\cdot249\end{pmatrix}=\begin{pmatrix}1820 \\ \: 2524 \\ \: 1614\end{pmatrix} \\ \text{Product }A\cdot B=\begin{pmatrix}Sean \\ Kevin \\ Bill\end{pmatrix}\begin{pmatrix}1820 \\ 2524 \\ 1614\end{pmatrix} \end{gathered}[/tex]Find the average rate of change of the following function from t = 1 to t=2.5h(t) = 148 – 16t
The average rate of change of the function from t=1 to t=2.5 is given by:
[tex]\frac{h(2.5)-h(1)}{2.5-1}=\frac{h(2.5)-h(1)}{1.5}[/tex]It is given that:
[tex]\begin{gathered} h(t)=148-16t \\ h(2.5)=148-16\times2.5=108 \\ h(1)=148-6=142 \end{gathered}[/tex]Substitute the values to get:
[tex]\frac{h(2.5)-h(1)}{1.5}=\frac{108-142}{1.5}=\frac{-68}{3}\approx-22.6667[/tex]Hence the rate of change is -22.6667.
Determine the midpoint between A(2,13) and O (-4,3)
The midpoint between two points can be found by averaging their coordinates. This is done below:
[tex]\begin{gathered} x_m\text{ = }\frac{x_1+x_2}{2} \\ y_m\text{ = }\frac{y_1+y_2}{2} \end{gathered}[/tex]Using the above expressions we can apply the coordinates of the points we want to find, A(2,13) and O(-4,3).
[tex]\begin{gathered} x_m\text{ = }\frac{2\text{ -4}}{2} \\ x_m\text{ = }\frac{-2}{2} \\ x_m\text{ = -1} \end{gathered}[/tex][tex]\begin{gathered} y_m\text{ = }\frac{3+13}{2} \\ y_m\text{ = }\frac{16}{2} \\ y_m\text{ = 8} \end{gathered}[/tex]The coordinates of the midpoint are (-1,8).
Determine whether the equation represents an exponential growth function, anexponential decay function, and give the percent growth or decay.17. y = 18(1.3)^t
A exponential growth or decay function has the next general form:
[tex]y=a(1\pm r)^t[/tex]If it is :
(1+r) , (>1) the function growth
(1-r) , (<1) the function decay
------
The given equation:
[tex]y=18(1.3)^t[/tex]As the (1+r) is equal to 1.3 (> 1) then it is a exponential growth function.In (1+r) the r is the percent of growth, then for the given equation you have:
[tex]\begin{gathered} 1+r=1.3 \\ r=1.3-1 \\ \\ r=0.3 \end{gathered}[/tex]The percent of decay is 0.3 or 30%A triangle has squares on its three sides as shown below. What is the value of x? 4 centimeters 7 centimeters 5 centimeters 3 centimeters
you can make pancakes with just bananas and eggs : serves 4 people with 6 eggs 2 bananas. how many eggs and bananas do u need to serve 6 people?
Given:
To prepare a pancake that serves 4 people, we need 6 eggs and 2 bananas.
Required:
The number of eggs and bananas that serves 6 people
By comparison,
If we need 6 eggs to prepare a pancake that serves 4 people, the number of people that 1 egg would serve is:
[tex]\begin{gathered} k\text{ = }\frac{4\text{ people}}{6\text{ eggs}} \\ =\text{ }\frac{2}{3}\text{ people/ egg} \end{gathered}[/tex]Similarly, If we need 2 bananas to prepare a pancake that serves 4 people, the number of people that 1 banana would serve is:
[tex]\begin{gathered} k_2\text{ = }\frac{4\text{ people}}{2\text{ bananas}} \\ =\text{ 2 people/banana} \end{gathered}[/tex]The number of eggs that serves 6 people:
[tex]\begin{gathered} =\text{ 6 people }\times\frac{3}{2}\text{ egg/people} \\ =\text{ 9 eggs} \end{gathered}[/tex]The number of bananas that serves 6 people:
[tex]\begin{gathered} =\text{ 6 people }\times\text{ }\frac{1}{2}\text{ banana/ people} \\ =\text{ 3 bananas} \end{gathered}[/tex]Answer:
9 eggs are needed
3 bananas are needed
I need help with this questions I don’t. Get it
You will need 275 ml of the 90% solution
Explanation:Let the amount of the 90% alcohol be x
Amount of the 30% alcohol solution = 385 ml
The amount of the mixture = 385 + x
(30% of 385) + (90% of x) = 55% of (385+x)
[tex]\begin{gathered} (\frac{30}{100}\times385)+(\frac{90}{100}\times x)=\frac{55}{100}\times(385+x) \\ \\ (0.3\times385)+(0.9\times x)=0.55(385+x) \\ \\ 115.5+0.9x=211.75+0.55x \\ \\ 0.9x-0.55x=211.75-115.5 \\ \\ 0.35x=96.25 \\ \\ x=\frac{96.25}{0.35} \\ \\ x=275 \\ \\ \end{gathered}[/tex]You will need 275 ml of the 90% solution
I need help, I did 1-2b, but i do not mind someone answering it either way so I can double check, but I am mainly stuck with 2c and if someone can tell me the answer and as to why, it would mean a lot and you can get brainlest if it is the right answer :)(Not a multiple choice question)
Absolute Minimum: an absolute minimum point is a point where the function obtains its least possible value.
The given function :
[tex]f(x)=x^4-4x^3-x^2+12x-2[/tex]In the graph of the f(x) , the least value of x of the given curve is : (-0.939)
and the f(x) at x = (-0.939) is -10.065
The absolute minimum value is (x,y) = (-0.939, -10.065)
To round off in the nearest hundredth : (x, y) = (-0.94, -10.07)
Answer : (x, y) = (-0.94, -10.07)
shirts are 15% off. The original price of one shirt is $20. What is the total cost, in dollars, of a shirt, at the sales price, including a 10% sales tax?
The original price of the shirt is , 20 dollar.
It is given that the shirts are 15% off.
Therefore, the price of the shirt is ,
[tex]20-20\times\frac{15}{100}=17.[/tex]The price of the shirt is, 17 dollar after 15% off.
It is also given that there are 10% sales tax.
The total cost of the shirt is determined by including the sales tax in the price of the shirt after 15% off.
[tex]17+(17\times\frac{10}{100})=18.7[/tex]Thus, The total cost of shirt is calculated as, 18.7 dollar.
1. Abby baked 2-dozen brownies. She took 1 dozen to her scout meeting. Her family ate 8, and she put the rest in a container in the refrigerator. How can Abby find the number of brownies left in the refrigerator?
The number of brownies left in the refrigerator is 4.
How to calculate the value?It's important to note that 1 dozen = 12
In this case, Abby baked 2-dozen brownies, she took 1 dozen to her scout meeting and her family ate 8, and she put the rest in a container in the refrigerator.
Therefore, the remaining amount will be:
= 2 dozens - 1. dozen - 8
= (2 × 12) - 12 - 8
= 24 - 12 - 8
= 4
There'll be 4 left. This illustrates the concept of subtraction.
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The point (2, 4) is reflected over the x-axis. What are its new coordinates?Use the blank grid below it it helps.-6-54-321-6ch-4-3-2.-1O3N56-1-2-3--4--5-6O (2,-4)O (-2,-4)O (4,2)O (-2,4)
Let:
[tex]\begin{gathered} A=(x1,y1)=(2,4) \\ A^{\prime}=(x1^{\prime},y1^{\prime}) \end{gathered}[/tex]After a reflection over the x-axis:
[tex]A\to(x,-y)\to A^{\prime}=(2,-4)[/tex]Answer:
(2,-4)
What is the slope and y-intercept?
y=3x-2
Options:
Blank # 1
Blank # 2
The value of slope is 3 and the value of y - intercept is -2.
Slope and y intercept:
The slope refers the rate of change in y per unit change in x.
The y-intercept states the y-value when the x-value is 0.
Given,
Here we have the equation
y = 3x - 2
Now, we need to find the slope and y intercept of the equation.
We know that, the standard form of the equation of the line is,
y = mx + b
Where
m represents the slope
b represents the y-intercept.
So, we have to rewrite the given equation as,
y = 3x + (-2)
So, while comparing the given equation with standard form, then we get,
the value of the slope is 3 and the value of the y intercept is -2.
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can i get some help please?
i need help on number 7. Please use 4 points
In order to graph this equation, we need at least two points that are solution to the equation.
To find these points, we can choose values for x and then calculate the corresponding values of y.
Choosing the x-values of -2, -1, 0 and 1, we have:
[tex]\begin{gathered} x=-2\colon \\ y=-\frac{5}{2}\cdot(-2)-1 \\ y=5-1 \\ y=4 \\ \\ x=-1\colon \\ y=-\frac{5}{2}(-1)-1 \\ y=2.5-1 \\ y=1.5 \\ \\ x=0\colon \\ y=-\frac{5}{2}\cdot0-1 \\ y=-1 \\ \\ x=1\colon \\ y=-\frac{5}{2}\cdot1-1 \\ y=-2.5-1 \\ y=-3.5 \end{gathered}[/tex]So we have the points (-2, 4), (-1, 1.5), (0, -1) and (1, -3.5). Graphing these points and the line that passes through them, we have:
2,000 deposit,compound interest,compounded anually,at 6% for 2 years. What is the total balance(A=Principal+Interest)?
Given a principal P, compounded anually at r% for t years. Then the
a carpentar has 16 1/2m of wood he cuts the wood into peices that are each 2 3/4m long PLSSSSS HURRY!!!!!!!!
The most appropriate choice for fraction will be given by
6 pieces of wood are cut by the carpenter
What is a fraction?
Suppose there is a collection of objects and some part of the objects are taken from the collection. The part which has been taken is called fraction. In other words, part of a whole is called fraction.
The upper part of the fraction is called numerator and the lower part of the fraction is called denominator.
Total length of wood = [tex]16\frac{1}{2}[/tex] m
= [tex]\frac{33}{2}[/tex] m
Length of one piece of a wood = [tex]2\frac{3}{4}[/tex] m = [tex]\frac{11}{4}[/tex]
Number of pieces of wood cut by carpenter = [tex]\frac{33}{2}[/tex] ÷ [tex]\frac{11}{4}[/tex]
= [tex]\frac{33}{2}[/tex] [tex]\times \frac{4}{11}[/tex]
= 6
6 pieces of wood are cut by the carpenter
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1 Select the correct answer from each drop-down menu. 500 N 520 and = < In the figures
x = (internal angle)
y,z = (externals)
Then
Angle x= < x= 180° - 50° -45° = 85°
Angle y= 180° - (180° - Angle z =
Then answers are
Angle x= 85°
Angle y= 137°
Angle z= 128°
OB. 1OC.If X = 24 inches, Y = 45 inches, and Z= 51 inches, what is the tangent of ZA?OA. 19715NOD. 1B
Given that
We have a right-angled triangle and have to find angle A's tangent.
Explanation -
The triangle is shown as
Here we have,
X = 24 inches
Y = 45 inches
Z = 51 inches
Then, the tangent of angle A will be
[tex]\begin{gathered} The\text{ formula for the tangent is } \\ tan=\frac{Perpendicular}{Base} \\ \\ tan=\frac{P}{B} \\ For\text{ angle A thevalues are, P = 45 and B = 24} \\ Then, \\ tanA=\frac{45}{24} \\ \\ tanA=\frac{15}{8} \end{gathered}[/tex]So the correct option is B.
Final answer -
Therefore the final answer is 15/8How many offices are between 41 and 50 meters ?
Solution
For this case we want to find the number of offices between 41 and 50 m and the answer is:
2 meters
PLEASE HELP ASAP! What is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola?
A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.
What is hyperbola?A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set. A hyperbola is made up of two mirror images of one another that resemble two infinite bows.These two sections are known as connected components or branches. A series of points in a plane that are equally spaced out from a directrix or focus is known as parabolas. The difference in distances between a group of points that are situated in a plane and two fixed points—which is a positive constant—is what is referred to as the hyperbola.Therefore, a hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.
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he center of the circle below is at P. If arc AB measures 86 °, then what is the measure of the angle < APB ?
Answer:
D. 86°
Explanation:
Given:
• The center of the circle = P
,• The measure of arc AB = 86°
We want to find the measure of the angle APB.
By Circle's theorem: The measure of an arc is equal to the measure of the central angle subtended by the same arc.
Applying this theorem, we have that:
[tex]\begin{gathered} m\angle APB=m\widehat{AB} \\ \implies m\angle APB=86\degree \end{gathered}[/tex]The measure of the angle APB is 86 degrees.
Option D is correct.
LanaCharles almn on the coordinate plane what is the perimeter of a ALMN round to the nearest unit
The Solution:
Given the graph below:
We are required to find the perimeter of the triangle LMN rounded to the nearest unit.
Step 1:
Find the distance LM, where L(-3,2) and M(3,5)
By the formula for distance between two points, we have
[tex]LM=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where,
[tex]\begin{gathered} x_1=-3 \\ y_1=2 \\ x_2=3 \\ y_2=5 \end{gathered}[/tex]Substituting, we get
[tex]LM=\sqrt[]{(3--3)^2+(5-2)^2}=\text{ }\sqrt[]{6^2+7^2}=\text{ }\sqrt[]{85}=9.2195[/tex]Step 2:
Find the distance LN:
[tex]LN=12[/tex]Step 3:
Find the distance MN, where M(3,5) and N(9,2)
[tex]MN=\sqrt[]{(9-3)^2+(2-5)^2}=\text{ }\sqrt[]{6^2+(-3)^2}=\text{ }\sqrt[]{45}=6.7082[/tex]Step 4:
The perimeter is:
[tex]\text{ Perimeter=LM+MN+LN=9.2195+6.7082+12=27.9277}\approx28\text{ units}[/tex]Therefore, the correct answer is 28 units.
find the measure of each of the other six angles
The measure of angle 1 is 71º, we can find this, because angle 1 and angle x form a straight line of 180º, so 180º - 109º = 71º
The measure of angle 2 is also 71º, we can use the vertical angles propierty, then m∠1 = m∠2
The measure of angle 3 is 109º, we can use again the vertical angles theorem to find that m∠x = m∠3
Themeasure of angle 7 is 109º. We need to use the alternating exterior angles theorem. Since angle x and angle 7 are not between the parallel lines they're exterior angles; and since they're on opposite sides of the transversal line, they're alternates. Then the theorem says that m∠x = m∠7
The measure of angle 6 is 71º, again we're using the fact that angle 7 and angle 6 forms a straight line, then m∠6 = 180º - 109º = 71º
Now we can find the lasts two measures using the vertical angles theorem.
The measure of angle 5 is 71º, because m∠6 = m∠5
The measure of angle 4 is 109º, because m∠7 = m∠4
Use the multiplication method to solve the following systems of equations. c + 3t = 7 and 3c – 2t = –12
5x – 4z = 15 and –3x + 2z = 21
–4m + 3n = 50 and 2m + n = 10
2p – 4q = 18 and –3p + 5q = 22
3a + 4b = 51 and 2a + 3b = 37
After solving the system of equations we get the values as:
c=-2 and t=3x= -57 and z=-75m=-2 and n=14p=-89 and q=-49a=5 and b=9Given the equations are as follows, we need to solve them using multiplication method:
c+3t=7 and 3c-2t=-12take c+3t=7
rearrange the terms.
c = 7-3t
substitute c value in other equation.
3(7-3t)-2t=-12
21-9t-2t=-12
21-11t=-12
-11t = -12-21
-11t=-33
t=33/11
t=3
now substitute t value in c = 7-3t
c = 7-3(3)
c=7-9
c=-2
hence t and c values are 3 and -2.
5x – 4z = 15 and –3x + 2z = 21take 5x – 4z = 15
5x = 15+4z
x=15+4z/5
substitute x value in other equation.
-3(15+4z/5)+2z=21
-45-12z+10z=105
-45-2z=105
-2z=105+45
z=-75
substitute z value in x=15+4z/5
x=15+4(-75)/5
x=-57
hence x and z values are -57 and -75.
–4m + 3n = 50 and 2m + n = 10consider, -4m+3n=50
3n = 50+4m
n=50+4m/3
substitute n value in other equation.
2m+n=10
2m+50+4m/3 = 10
6m+50+4m=30
10m=30-50
10m=-20
m=-2
substitute m value in n=50+4m/3
n = 50+4(-2)/3
n = 50-8/3
n = 42/3
n = 14
hence m and n values are -2 and 14.
2p – 4q = 18 and –3p + 5q = 22consider 2p - 4q = 18
2p = 18+4q
p = 9+2q
substitute p value in other equation.
-3p+5q=22
-3(9+2q)+5q=22
-27-6q+5q=22
-27-q=22
-q = 22+27
q = -49
now p = 9+2q
p = 9+2(-49)
p = 9-98
p=-89
hence p and q values are -89 and -49.
3a + 4b = 51 and 2a + 3b = 37consider 3a + 4b = 51
3a = 51-4b
a=51-4b/3
substitute a value in other equation.
2(51-4b/3)+3b=37
102-8b+9b=111
102+b=111
b=111-102
b=9
now, a=51-4(9)/3
a = 51-36/3
a = 15/3
a = 5
hence a and b value are 5 and 9.
Therefore, we solved the required system of equations.
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I need help understanding slope
we know that
the formula to calculate teh slope between two points is equal to
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]where
(x1,y1) is one point
and
(x2,y2) is the other point
substitute the values in the formula and solve for m
Example
you have the points
(1,4) and (3,2)
so
(x1,y1)=(1,4)
(x2,y2)=(3,2)
substitute in te formula
m=(2-4)/(3-1)
m=-2/2
m=-1
the slope is -1
