Answer
point-slope form: $y+2=-5(x+4)$
slope-intercept form: $y=-5x-22$
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 $-5$ and passes through the point $(-4, -2)$.
Substitute these values into the point-slope form above to obtain:
$y-(-2)=-5[x-(-4)]
\\y+2 = -5(x+4)$
(b) slope-intercept form
Substitute the slope $-5$ to $m$ to obtain the tentative equation:
$y=-5x+b$
The line passes through $(-4, -2)$.
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:
$y=-5x+b
\\-2 = -5(-4) + b
\\-2 = 20 + b
\\-2-20 = b
\\-22= b$
Thus, the equation of the line is $y=-5x-22$.
