Question

which of the following equations does the graph below represent? answer attempt 1 out of 3 \\(\circ\\) \\(x + 8y = 40\\) \\(\circ\\) \\(-10x + 8y = 40\\) \\(\circ\\) \\(-10x + y = 40\\) \\(\circ\\) \\(-10x - 8y = 40\\)

Explanation:

Step1: Find slope and intercept

From graph, y-intercept \( b = 5 \)? Wait, no, looking at the graph, when \( x=0 \), \( y=5 \)? Wait, no, the graph crosses y-axis at (0,5)? Wait, no, the grid: each square is 2? Wait, no, let's check points. The line crosses y-axis at (0,5)? Wait, no, let's take two points: (-4, 0) and (0, 5)? Wait, no, slope \( m = \frac{y2 - y1}{x2 - x1} \). Let's take (-4, 0) and (0, 5). Then slope \( m = \frac{5 - 0}{0 - (-4)} = \frac{5}{4} \)? Wait, no, maybe I misread. Wait, the options are linear equations. Let's convert each option to slope-intercept form \( y = mx + b \).

Step2: Convert each option

1. \( x + 8y = 40 \): \( 8y = -x + 40 \) → \( y = -\frac{1}{8}x + 5 \). Slope negative, but graph has positive slope. Eliminate.
2. \( -10x + y = 40 \): \( y = 10x + 40 \). Slope 10, y-intercept 40. Too steep, graph has smaller slope. Eliminate.
3. \( -10x + 8y = 40 \): \( 8y = 10x + 40 \) → \( y = \frac{10}{8}x + 5 \) → \( y = \frac{5}{4}x + 5 \). Slope \( \frac{5}{4} \), y-intercept 5. Let's check if (-4, 0) is on this line: \( y = \frac{5}{4}(-4) + 5 = -5 + 5 = 0 \). Correct.
4. \( -10x - 8y = 40 \): \( -8y = 10x + 40 \) → \( y = -\frac{10}{8}x - 5 \). Slope negative, eliminate.

Step3: Verify with points

Check (-4, 0) in \( -10x + 8y = 40 \): \( -10(-4) + 8(0) = 40 + 0 = 40 \). Correct. Check (0,5): \( -10(0) + 8(5) = 0 + 40 = 40 \). Correct.

Answer:

\( -10x + 8y = 40 \) (the third option)