Question

select the correct answer.
which equation represents a line that is perpendicular to line fg?
a. $y = -\frac{1}{2}x + 5$
b. $y = \frac{1}{2}x + 2$
c. $y = -2x - 3$
d. $y = 2x - 6$

Explanation:

Step1: Find slope of FG

Points \( F(-5, 1) \) (wait, looking at graph: F is at (-5,1)? Wait, no, let's check coordinates. From graph, F is at (-5,1)? Wait, no, the grid: F is at x=-5, y=1? Wait, no, let's see: F is at (-5,1)? Wait, actually, looking at the graph, F is at (-5,1)? Wait, no, let's get coordinates correctly. Let's take F: x=-5, y=1? Wait, no, the line passes through F (let's see, F is at (-5,1)? Wait, no, the y-intercept is 4? Wait, the line FG: let's take two points. Let's take F: from the graph, F is at (-5,1)? Wait, no, maybe F is at (-5,1)? Wait, no, let's check G: G is at (9,8)? Wait, no, the graph: G is at (9,8)? Wait, no, the x-axis: G is at x=9, y=8? Wait, no, the grid lines: each square is 1 unit. So F is at (-5,1)? Wait, no, let's take F: x=-5, y=1? Wait, no, the line passes through (0,4) (y-intercept) and F: let's see, when x=-5, y=1? Wait, no, let's calculate slope. Let's take two points: F(-5,1) and G(9,8)? Wait, no, maybe F is at (-5,1) and G is at (9,8)? Wait, no, let's do it properly. Let's take F: x=-5, y=1? Wait, no, the line goes through (0,4) (y-intercept 4) and F: let's see, when x=-8, y=0? Wait, the line crosses x-axis at (-8,0). So two points: (-8,0) and (0,4). So slope \( m = \frac{4 - 0}{0 - (-8)} = \frac{4}{8} = \frac{1}{2} \). So slope of FG is \( \frac{1}{2} \).

Step2: Slope of perpendicular line

Perpendicular lines have slopes that are negative reciprocals. So if slope of FG is \( \frac{1}{2} \), then slope of perpendicular line is \( -2 \) (since negative reciprocal of \( \frac{1}{2} \) is \( -2 \)).

Step3: Check options

Now check the options:

A. \( y = -\frac{1}{2}x + 5 \): slope \( -\frac{1}{2} \) – not -2.

B. \( y = \frac{1}{2}x + 2 \): slope \( \frac{1}{2} \) – same as FG, parallel.

C. \( y = -2x - 3 \): slope \( -2 \) – which is negative reciprocal of \( \frac{1}{2} \).

D. \( y = 2x - 6 \): slope 2 – not -2.

So the correct answer is C.

Answer:

C. \( y = -2x - 3 \)