# Find the Slope and Y-Intercept (12,-2) , (-24,6)

(12,-2) , (-24,6)
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=6-(-2)-24-(12)
Simplify.
Cancel the common factor of 6-(-2) and -24-(12).
Rewrite -24 as -1(24).
m=6-(-2)-1⋅24-(12)
Factor -1 out of -1(24)-(12).
m=6-(-2)-1(24+12)
Reorder terms.
m=6-2⋅-1-1(24+12)
Factor 2 out of 6.
m=2(3)-2⋅-1-1(24+12)
Factor 2 out of -2⋅-1.
m=2(3)+2(1)-1(24+12)
Factor 2 out of 2(3)+2(–1).
m=2(3+1)-1(24+12)
Cancel the common factors.
Factor 2 out of -1(24+12).
m=2(3+1)2(-1(12+6))
Cancel the common factor.
m=2(3+1)2(-1(12+6))
Rewrite the expression.
m=3+1-1(12+6)
m=3+1-1(12+6)
m=3+1-1(12+6)
Simplify the numerator.
Multiply -1 by -1.
m=3+1-1(12+6)
Add 3 and 1.
m=4-1(12+6)
m=4-1(12+6)
Reduce the expression by cancelling the common factors.
Add 12 and 6.
m=4-1⋅18
Multiply -1 by 18.
m=4-18
Cancel the common factor of 4 and -18.
Factor 2 out of 4.
m=2(2)-18
Cancel the common factors.
Factor 2 out of -18.
m=2⋅22⋅-9
Cancel the common factor.
m=2⋅22⋅-9
Rewrite the expression.
m=2-9
m=2-9
m=2-9
Move the negative in front of the fraction.
m=-29
m=-29
m=-29
m=-29
Find the value of the y-intercept.
Substitute the value of m into the slope-intercept form of the equation, y=mx+b.
y=(-29)⋅x+b
Substitute the value of x into the slope-intercept form of the equation, y=mx+b.
y=(-29)⋅(12)+b
Substitute the value of y into the slope-intercept form of the equation, y=mx+b.
-2=(-29)⋅(12)+b
Rewrite the equation as (-29)⋅(12)+b=-2.
(-29)⋅(12)+b=-2
Simplify each term.
Cancel the common factor of 3.
Move the leading negative in -29 into the numerator.
-29⋅12+b=-2
Factor 3 out of 9.
-23(3)⋅12+b=-2
Factor 3 out of 12.
-23⋅3⋅(3⋅4)+b=-2
Cancel the common factor.
-23⋅3⋅(3⋅4)+b=-2
Rewrite the expression.
-23⋅4+b=-2
-23⋅4+b=-2
Combine -23 and 4.
-2⋅43+b=-2
Multiply -2 by 4.
-83+b=-2
Move the negative in front of the fraction.
-83+b=-2
-83+b=-2
Move all terms not containing b to the right side of the equation.
Add 83 to both sides of the equation.
b=-2+83
To write -2 as a fraction with a common denominator, multiply by 33.
b=-2⋅33+83
Combine -2 and 33.
b=-2⋅33+83
Combine the numerators over the common denominator.
b=-2⋅3+83
Simplify the numerator.
Multiply -2 by 3.
b=-6+83
Add -6 and 8.
b=23
b=23
b=23
b=23
The values of the slope and y-intercept are m=-29 and b=23.
m=-29
b=23
Find the Slope and Y-Intercept (12,-2) , (-24,6)

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