Question

line p goes through the points (-5, 9) and (1, -3). line q goes through the point (4, 7) and is perpendicular to line p.
graph line q.
graph with x-axis from -10 to 10 and y-axis from -10 to 10, grid lines present

Explanation:

Step1: Find slope of line p

Use slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $(-5, 9)$ and $(1, -3)$:
$m_p = \frac{-3 - 9}{1 - (-5)} = \frac{-12}{6} = -2$

Step2: Find slope of line q (perpendicular)

Perpendicular slopes are negative reciprocals: $m_q = \frac{1}{2}$

Step3: Use point - slope for line q

Point - slope: $y - y_1 = m(x - x_1)$. For point $(4, 7)$ and $m_q=\frac{1}{2}$:
$y - 7 = \frac{1}{2}(x - 4)$
Simplify: $y - 7 = \frac{1}{2}x - 2 \implies y = \frac{1}{2}x + 5$

Step4: Graph line q

Plot $(4, 7)$, then use slope $\frac{1}{2}$ (up 1, right 2 or down 1, left 2) to find other points (e.g., $(6, 8)$, $(2, 6)$) and draw the line.

Answer:

To graph line \( q \), first determine its equation: slope \( \frac{1}{2} \), equation \( y=\frac{1}{2}x + 5 \). Plot the point \( (4, 7) \), then use the slope to find additional points (e.g., \( (6, 8) \), \( (2, 6) \)) and draw the line through them.