(1,-19) , (-2,-7)

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=-7-(-19)-2-(1)

Simplify.

Simplify the numerator.

Multiply -1 by -19.

m=-7+19-2-(1)

Add -7 and 19.

m=12-2-(1)

m=12-2-(1)

Simplify the denominator.

Multiply -1 by 1.

m=12-2-1

Subtract 1 from -2.

m=12-3

m=12-3

Divide 12 by -3.

m=-4

m=-4

m=-4

Use the slope -4 and a given point (1,-19) to substitute for x1 and y1 in the point-slope form y-y1=m(x-x1), which is derived from the slope equation m=y2-y1x2-x1.

y-(-19)=(-4)(x-(1))

Simplify the equation and keep it in point-slope form.

y+19=-4⋅(x-1)

Simplify -4⋅(x-1).

Apply the distributive property.

y+19=-4x-4⋅-1

Multiply -4 by -1.

y+19=-4x+4

y+19=-4x+4

Move all terms not containing y to the right side of the equation.

Subtract 19 from both sides of the equation.

y=-4x+4-19

Subtract 19 from 4.

y=-4x-15

y=-4x-15

y=-4x-15

List the equation in different forms.

Slope-intercept form:

y=-4x-15

Point-slope form:

y+19=-4⋅(x-1)

Find the Equation Using Point-Slope Formula (1,-19) , (-2,-7)