Question

a. why are the lines whose equations are $y = \frac{1}{5}x + 6$ and $y = -5x - 3$ perpendicular?
b. use a graphing utility to graph the equations in a $-10, 10, 1$ by $-10, 10, 1$ viewing rectangle. do the lines appear to be perpendicular?
c. now use the zoom square feature of your utility. describe what happens to the graphs. explain why this is so

b. choose the correct graph below.
a.
b.
c.
d.

Explanation:

Step1: Identify slopes of lines

For $y=\frac{1}{5}x+6$, slope $m_1=\frac{1}{5}$; for $y=-5x-3$, slope $m_2=-5$.

Step2: Check perpendicularity condition

Multiply the slopes: $m_1 \times m_2 = \frac{1}{5} \times (-5) = -1$

Step3: Analyze non-square viewing rectangle

In $[-10,10,1]$ by $[-10,10,1]$, the x and y scales are stretched differently, so the right angle appears distorted.

Step4: Analyze zoom square feature

Zoom square makes x and y scales equal, so the perpendicular right angle appears correct.

Step5: Match graph for part b

Graph A shows the lines with a distorted (non-square) aspect ratio, matching the $[-10,10,1]$ viewing rectangle.

Answer:

a. The product of their slopes is -1, which is the condition for perpendicular lines.
b. A. <Graph A image description: Lines appear to not form a right angle due to non-square viewing rectangle>; No, the lines do not appear perpendicular in this viewing rectangle.
c. After using zoom square, the lines appear to form a right angle (perpendicular). This is because the zoom square feature makes the horizontal and vertical scales equal, so the true geometric relationship of perpendicular lines is visible.