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

(1,-19) , (-2,-7)
Find the slope of the line between (1,-19) and (-2,-7) using m=y2-y1x2-x1, which is the change of y over the change of x.
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)
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)
Solve for y.
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)