# Find the Slope and Y-Intercept (-2,4) , (3,1) (-2,4) , (3,1)
Find the value of the slope.
Slope is equal to the change in y over the change in x, or rise over run.
m=change in ychange in x
The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).
m=y2-y1x2-x1
Substitute in the values of x and y into the equation to find the slope.
m=1-(4)3-(-2)
Simplify.
Simplify the numerator.
Multiply -1 by 4.
m=1-43-(-2)
Subtract 4 from 1.
m=-33-(-2)
m=-33-(-2)
Simplify the denominator.
Multiply -1 by -2.
m=-33+2
Add 3 and 2.
m=-35
m=-35
Move the negative in front of the fraction.
m=-35
m=-35
m=-35
Find the value of the y-intercept.
Substitute the value of m into the slope-intercept form of the equation, y=mx+b.
y=(-35)⋅x+b
Substitute the value of x into the slope-intercept form of the equation, y=mx+b.
y=(-35)⋅(-2)+b
Substitute the value of y into the slope-intercept form of the equation, y=mx+b.
4=(-35)⋅(-2)+b
Rewrite the equation as (-35)⋅(-2)+b=4.
(-35)⋅(-2)+b=4
Multiply (-35)(-2).
Multiply -2 by -1.
2(35)+b=4
Combine 2 and 35.
2⋅35+b=4
Multiply 2 by 3.
65+b=4
65+b=4
Move all terms not containing b to the right side of the equation.
Subtract 65 from both sides of the equation.
b=4-65
To write 4 as a fraction with a common denominator, multiply by 55.
b=4⋅55-65
Combine 4 and 55.
b=4⋅55-65
Combine the numerators over the common denominator.
b=4⋅5-65
Simplify the numerator.
Multiply 4 by 5.
b=20-65
Subtract 6 from 20.
b=145
b=145
b=145
b=145
The values of the slope and y-intercept are m=-35 and b=145.
m=-35
b=145
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