Answer
point-slope form: $y=-4(x+4)$
slope-intercept form: $y=-4x-16$
Work Step by Step
RECALL:
(1) The slope-intercept form of a line's equation is:
$y=mx+b$
where m = slope and b = y-intercept
(2) The point-slope form of a line's equation is:
$y-y_1=m(x-x_1)$
(a) point-slope form
The given line has a slope of $-4$ and passes through the point $(-4, 0)$.
Substitute these values into the point-slope form above to obtain:
$y-0=-4[x-(-4)]
\\y = -4(x+4)$
(b) slope-intercept form
Substitute the slope $-4$ to $m$ to obtain the tentative equation:
$y=-4x+b$
The line passes through $(-4, 0)$.
This means that the coordinates of this point satisfy the equation of the line. Substitute the x and y-coordinates of this point into the tentative equation to obtain:
$y=-4x+b
\\0 = -4(-4) + b
\\0 = 16 + b
\\0-16 = b
\\-16= b$
Thus, the equation of the line is $y=-4x-16$.
