Question

2.2.3 quiz: parallel and perpendicular lines what is the equation of a line that passes through (8, -5) and is parallel to the graphed line? a. $y = \frac{3}{4}x - 11$ b. $y = -\frac{4}{3}x - \frac{47}{3}$ c. $y = \frac{3}{4}x + 1$ d. $y = -\frac{4}{3}x + \frac{17}{4}$

Explanation:

Step1: Find slope of graphed line

Identify two points on the line: $(4,0)$ and $(0,-3)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{0-(-3)}{4-0}=\frac{3}{4}$

Step2: Use point-slope form

Parallel lines have equal slopes. Use point $(8,-5)$: $y-y_1=m(x-x_1)$
$y-(-5)=\frac{3}{4}(x-8)$

Step3: Simplify to slope-intercept form

Expand and isolate $y$:
$y+5=\frac{3}{4}x - 6$
$y=\frac{3}{4}x - 6 - 5$
$y=\frac{3}{4}x - 11$

Answer:

A. $y = \frac{3}{4}x - 11$