# Find the Slope and Y-Intercept (8,-1) , (2,-8) (8,-1) , (2,-8)
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=-8-(-1)2-(8)
Simplify.
Simplify the numerator.
Multiply -1 by -1.
m=-8+12-(8)
Add -8 and 1.
m=-72-(8)
m=-72-(8)
Simplify the denominator.
Multiply -1 by 8.
m=-72-8
Subtract 8 from 2.
m=-7-6
m=-7-6
Dividing two negative values results in a positive value.
m=76
m=76
m=76
Find the value of the y-intercept.
Substitute the value of m into the slope-intercept form of the equation, y=mx+b.
y=(76)x+b
Substitute the value of x into the slope-intercept form of the equation, y=mx+b.
y=(76)⋅(8)+b
Substitute the value of y into the slope-intercept form of the equation, y=mx+b.
-1=(76)⋅(8)+b
Rewrite the equation as (76)⋅(8)+b=-1.
(76)⋅(8)+b=-1
Simplify each term.
Cancel the common factor of 2.
Factor 2 out of 6.
72(3)⋅8+b=-1
Factor 2 out of 8.
72⋅3⋅(2⋅4)+b=-1
Cancel the common factor.
72⋅3⋅(2⋅4)+b=-1
Rewrite the expression.
73⋅4+b=-1
73⋅4+b=-1
Combine 73 and 4.
7⋅43+b=-1
Multiply 7 by 4.
283+b=-1
283+b=-1
Move all terms not containing b to the right side of the equation.
Subtract 283 from both sides of the equation.
b=-1-283
To write -1 as a fraction with a common denominator, multiply by 33.
b=-1⋅33-283
Combine -1 and 33.
b=-1⋅33-283
Combine the numerators over the common denominator.
b=-1⋅3-283
Simplify the numerator.
Multiply -1 by 3.
b=-3-283
Subtract 28 from -3.
b=-313
b=-313
Move the negative in front of the fraction.
b=-313
b=-313
b=-313
The values of the slope and y-intercept are m=76 and b=-313.
m=76
b=-313
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