(-2,12) , (6,16)

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

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)