# Find the Slope and Y-Intercept (-2,12) , (6,16) (-2,12) , (6,16)
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=16-(12)6-(-2)
Simplify.
Reduce the expression by cancelling the common factors.
Cancel the common factor of 16-(12) and 6-(-2).
Rewrite 16 as -1(-16).
m=-1⋅-16-(12)6-(-2)
Factor -1 out of -1(-16)-(12).
m=-1(-16+12)6-(-2)
Reorder terms.
m=-1(-16+12)6-2⋅-1
Factor 2 out of -1(-16+12).
m=2(-1(-8+6))6-2⋅-1
Cancel the common factors.
Factor 2 out of 6.
m=2(-1(-8+6))2(3)-2⋅-1
Factor 2 out of -2⋅-1.
m=2(-1(-8+6))2(3)+2(1)
Factor 2 out of 2(3)+2(–1).
m=2(-1(-8+6))2(3+1)
Cancel the common factor.
m=2(-1(-8+6))2(3+1)
Rewrite the expression.
m=-1(-8+6)3+1
m=-1(-8+6)3+1
m=-1(-8+6)3+1
Add -8 and 6.
m=-1⋅-23+1
m=-1⋅-23+1
Simplify the denominator.
Multiply -1 by -1.
m=-1⋅-23+1
Add 3 and 1.
m=-1⋅-24
m=-1⋅-24
Reduce the expression by cancelling the common factors.
Multiply -1 by -2.
m=24
Cancel the common factor of 2 and 4.
Factor 2 out of 2.
m=2(1)4
Cancel the common factors.
Factor 2 out of 4.
m=2⋅12⋅2
Cancel the common factor.
m=2⋅12⋅2
Rewrite the expression.
m=12
m=12
m=12
m=12
m=12
m=12
Find the value of the y-intercept.
Substitute the value of m into the slope-intercept form of the equation, y=mx+b.
y=(12)x+b
Substitute the value of x into the slope-intercept form of the equation, y=mx+b.
y=(12)⋅(-2)+b
Substitute the value of y into the slope-intercept form of the equation, y=mx+b.
12=(12)⋅(-2)+b
Rewrite the equation as (12)⋅(-2)+b=12.
(12)⋅(-2)+b=12
Cancel the common factor of 2.
Factor 2 out of -2.
12⋅(2(-1))+b=12
Cancel the common factor.
12⋅(2⋅-1)+b=12
Rewrite the expression.
-1+b=12
-1+b=12
Move all terms not containing b to the right side of the equation.
Add 1 to both sides of the equation.
b=12+1
Add 12 and 1.
b=13
b=13
b=13
The values of the slope and y-intercept are m=12 and b=13.
m=12
b=13
Find the Slope and Y-Intercept (-2,12) , (6,16)   ## Download our App from the store

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