point-slope form: $y+3=-2x$ slope-intercept form: $y=-2x-3$
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 $-2$ and passes through the point $(0, -3)$. Substitute these values into the point-slope form above to obtain: $y-(-3)=-2(x-0) \\y+3 = -2(x)$ (b) slope-intercept form Substitute the slope $-2$ to $m$ to obtain the tentative equation: $y=-2x+b$ The line passes through $(0, -3)$. 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: $y=-2x+b \\-3 = -2(0) + b \\-3 = 0 + b \\-3= b$ Thus, the equation of the line is $y=-2x-3$.