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The equation y=(3)/(2)(x-8) is graphed in the xy-plane. Which of the following equations will have a graph that is parallel to the graph of the given equation and have an x intercept on the negative x-axis? Choose 1 answer: (A) y=(3)/(2)(x+8) (B) y=(3)/(2)x-8 (C) y=-(2)/(3)(x+8) (D) y=-(2)/(3)x-8

The equation y=32(x−8) y=\frac{3}{2}(x-8) is graphed in the xy x y -plane. Which of the following equations will have a graph that is parallel to the graph of the given equation and have an x x intercept on the negative x x -axis?\newlineChoose 11 answer:\newline(A) y=32(x+8) y=\frac{3}{2}(x+8) \newline(B) y=32x−8 y=\frac{3}{2} x-8 \newline(C) y=−23(x+8) y=-\frac{2}{3}(x+8) \newline(D) y=−23x−8 y=-\frac{2}{3} x-8

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Q. The equation y=32(x−8) y=\frac{3}{2}(x-8) is graphed in the xy x y -plane. Which of the following equations will have a graph that is parallel to the graph of the given equation and have an x x intercept on the negative x x -axis?\newlineChoose 11 answer:\newline(A) y=32(x+8) y=\frac{3}{2}(x+8) \newline(B) y=32x−8 y=\frac{3}{2} x-8 \newline(C) y=−23(x+8) y=-\frac{2}{3}(x+8) \newline(D) y=−23x−8 y=-\frac{2}{3} x-8
  1. Find equation with same slope: We need to find an equation with a slope that is the same as the slope of the given equation y=(32)(x−8)y=\left(\frac{3}{2}\right)(x-8) to ensure the graphs are parallel. The slope of the given equation is 32\frac{3}{2}.
  2. Analyze options: The xx-intercept occurs when y=0y=0. For the graph to have an xx-intercept on the negative xx-axis, the xx-value at this intercept must be negative.
  3. Option A: Let's analyze the options one by one to see which one satisfies both conditions:\newline(A) y=(32)(x+8)y=\left(\frac{3}{2}\right)(x+8) - This equation has the same slope as the given equation, but the x-intercept would be at x=−8x=-8, which is on the negative x-axis. This is a potential correct answer.
  4. Option B: (B) y=32x−8y=\frac{3}{2}x-8 - This equation has the same slope as the given equation, but the y-intercept is −8-8, not the x-intercept. We need to find the x-intercept by setting y=0y=0 and solving for xx: 0=32x−8⇒x=1630=\frac{3}{2}x-8 \Rightarrow x=\frac{16}{3}, which is positive. So, this option does not satisfy the condition of having an x-intercept on the negative x-axis.
  5. Option C: (C) y=−(23)(x+8)y=-\left(\frac{2}{3}\right)(x+8) - This equation has a different slope (−23)\left(-\frac{2}{3}\right) from the given equation (32)\left(\frac{3}{2}\right), so the graphs will not be parallel. This option is incorrect.
  6. Option D: (D) y=−(23)x−8y=-\left(\frac{2}{3}\right)x-8 - This equation also has a different slope (−23)\left(-\frac{2}{3}\right) from the given equation (32)\left(\frac{3}{2}\right), so the graphs will not be parallel. This option is incorrect as well.

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