line st and point v are shown on the graph. line vw is to be drawn on the graph such that it is…

line st and point v are shown on the graph. line vw is to be drawn on the graph such that it is perpendicular to line st. if the coordinates of point w are (-1, y), what is the value of y? -7 -5 2 3

Answer

Explanation:

Step1: Find slope of line ST

Let (S(-5,0)) and (T(5,2)). Slope formula is (m = \frac{y_2 - y_1}{x_2 - x_1}). So (m_{ST}=\frac{2 - 0}{5-(-5)}=\frac{2}{10}=\frac{1}{5}).

Step2: Find slope of line VW

If two lines are perpendicular, the product of their slopes is - 1. Let the slope of line (VW) be (m_{VW}). Then (m_{ST}\times m_{VW}=-1). Since (m_{ST}=\frac{1}{5}), (m_{VW}=-5).

Step3: Use slope - formula for line VW

Let (V(0, - 2)) and (W(-1,y)). Using the slope formula (m=\frac{y_2 - y_1}{x_2 - x_1}), we have (m_{VW}=\frac{y-(-2)}{-1 - 0}). Since (m_{VW}=-5), then (\frac{y + 2}{-1}=-5).

Step4: Solve for y

Cross - multiply: (y + 2=5). Subtract 2 from both sides: (y=3).