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The equation 2y+3x=-10 is graphed in the xy-plane. Which of the following equations has a graph that is parallel to the graph of the given equation? Choose 1 answer: (A) y=-(2)/(3)x+(5)/(2) (B) y=(2)/(3)x-5 (c) y=(3)/(2)x-5 (D) y=-(3)/(2)x+(5)/(2)

The equation 2y+3x=−10 2 y+3 x=-10 is graphed in the xy x y -plane. Which of the following equations has a graph that is parallel to the graph of the given equation?\newlineChoose 11 answer:\newline(A) y=−23x+52 y=-\frac{2}{3} x+\frac{5}{2} \newline(B) y=23x−5 y=\frac{2}{3} x-5 \newline(C) y=32x−5 y=\frac{3}{2} x-5 \newline(D) y=−32x+52 y=-\frac{3}{2} x+\frac{5}{2}

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Full solution

Q. The equation 2y+3x=−10 2 y+3 x=-10 is graphed in the xy x y -plane. Which of the following equations has a graph that is parallel to the graph of the given equation?\newlineChoose 11 answer:\newline(A) y=−23x+52 y=-\frac{2}{3} x+\frac{5}{2} \newline(B) y=23x−5 y=\frac{2}{3} x-5 \newline(C) y=32x−5 y=\frac{3}{2} x-5 \newline(D) y=−32x+52 y=-\frac{3}{2} x+\frac{5}{2}
  1. Parallel lines and slope: Two lines are parallel if they have the same slope. The given equation is 2y+3x=−102y + 3x = -10. To find its slope, we need to write it in slope-intercept form, which is y=mx+by = mx + b, where mm is the slope.
  2. Converting the equation to slope-intercept form: First, we solve for yy in the given equation. Subtract 3x3x from both sides to get 2y=−3x−102y = -3x - 10.
  3. Finding the slope of the given line: Next, divide every term by 22 to solve for yy. This gives us y=−32x−5y = -\frac{3}{2}x - 5. Now we have the slope of the given line, which is −32-\frac{3}{2}.
  4. Checking the options for the same slope: We need to find the equation among the choices that has the same slope, −32-\frac{3}{2}. Let's check each option:\newline(A) y=−(23)x+(52)y = -\left(\frac{2}{3}\right)x + \left(\frac{5}{2}\right) has a slope of −23-\frac{2}{3}.\newline(B) y=(23)x−5y = \left(\frac{2}{3}\right)x - 5 has a slope of 23\frac{2}{3}.\newline(C) y=(32)x−5y = \left(\frac{3}{2}\right)x - 5 has a slope of 32\frac{3}{2}.\newline(D) y=−(32)x+(52)y = -\left(\frac{3}{2}\right)x + \left(\frac{5}{2}\right) has a slope of −32-\frac{3}{2}.
  5. Identifying the parallel equation: The only equation with a slope of −32-\frac{3}{2}, which is the same as the slope of the given equation, is option (D) y=−(32)x+(52)y = -\left(\frac{3}{2}\right)x + \left(\frac{5}{2}\right). Therefore, the graph of this equation is parallel to the graph of the given equation.

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