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 $y=-5x-22$.