Write an equation of the line that passes through the point (–4, 6) with slope –4.

Given:

Points ( -4, 6 )

x1 = -4

y1 = 6

m = -4

Write the equation of the line.
The equation of the line can be written in point-slope form and slope-intercept form

Formula for the point-slope form:

y -y1 = m (x - x1)

Formula for the slope-intercept form

y = mx + b

Solution:

Solve for point-slope form first, before going to slope-intercept form.

Substitute the given values of x1, m and y1 to the formula for the point-slope form.

y - 6 = -4 ( x - ( -4) )

y - 6 = -4 (x + 4)

In order to equate to slope-intercept form, we simply need to distribute -4 to each value inside the parenthesis, and then transpose -6 to the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.

y - 6 = -4 (x + 4)

y - 6 = -4x - 16

y = -4x - 16 + 6

y = -4x - 10

Final answer:

point-slope form: y - 6 = -4 (x + 4)

slope-intercept form: y = -4x - 10