Answer
point-slope form: $y+3=-3(x+2)$
slope-intercept form: $y=-3x-9$
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 $-3$ and passes through the point $(-2, -3)$.
Substitute these values into the point-slope form above to obtain:
$y-(-3)=-3[x-(-2)]
\\y+3 = -3(x+2)$
(b) slope-intercept form
Substitute the slope $-3$ to $m$ to obtain the tentative equation:
$y=-3x+b$
The line passes through $(-2, -3)$.
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:
$y=-3x+b
\\-3 = -3(-2) + b
\\-3 = 6 + b
\\-3-6 = b
\\-9= b$
Thus, the equation of the line is $y=-3x-9$.
