Question

the graph shows the relationship between the number of shares of stock from company a, x, and the number of shares of stock from company b, y, that simone can purchase. which equation could represent this relationship? a) $y = 8x + 12$ b) $8x + 12y = 480$ c) $y = 12x + 8$ d) $12x + 8y = 480$

Explanation:

Step1: Identify intercept points

The line crosses the x-axis at $(60, 0)$ and y-axis at $(0, 40)$.

Step2: Calculate slope

Slope $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{40 - 0}{0 - 60} = -\frac{2}{3}$

Step3: Write slope-intercept form

Using y-intercept $(0,40)$, $y = -\frac{2}{3}x + 40$

Step4: Convert to standard form

Multiply all terms by 3: $3y = -2x + 120$, rearrange to $2x + 3y = 120$. Multiply by 4: $8x + 12y = 480$

Step5: Verify with intercepts

Substitute $(60,0)$: $8(60)+12(0)=480$, true. Substitute $(0,40)$: $8(0)+12(40)=480$, true.

Answer:

B) $8x + 12y = 480$