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A line is graphed in the xy-plane shown. Which of the following is an equation of the line, if the line passes through the points (0, 0) and (2, -3) ? Choose 1 answer: (A) y=(3)/(2)x (B) y=(2)/(3)x (C) y=-(3)/(2)x (D) y=-(2)/(3)x

A line is graphed in the xy x y -plane shown. Which of the following is an equation of the line, if the line passes through the points (0,0)(0, 0) and (2,−3)(2, -3)??\newlineChoose 11 answer:\newline(A) y=32x y=\frac{3}{2} x \newline(B) y=23x y=\frac{2}{3} x \newline(C) y=−32x y=-\frac{3}{2} x \newline(D) y=−23x y=-\frac{2}{3} x

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Full solution

Q. A line is graphed in the xy x y -plane shown. Which of the following is an equation of the line, if the line passes through the points (0,0)(0, 0) and (2,−3)(2, -3)??\newlineChoose 11 answer:\newline(A) y=32x y=\frac{3}{2} x \newline(B) y=23x y=\frac{2}{3} x \newline(C) y=−32x y=-\frac{3}{2} x \newline(D) y=−23x y=-\frac{2}{3} x
  1. Calculate the slope: To find the equation of the line, we first need to calculate the slope mm using the two given points (0,0)(0, 0) and (2,−3)(2, -3). The slope is given by the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}.
  2. Substitute coordinates into slope formula: Substitute the coordinates of the points into the slope formula: m=−3−02−0=−32m = \frac{-3 - 0}{2 - 0} = \frac{-3}{2}.
  3. Determine the y-intercept: The slope of the line is m=−32m = -\frac{3}{2}. Since the line passes through the origin (0,0)(0, 0), the y-intercept bb is 00. Therefore, the equation of the line in slope-intercept form y=mx+by = mx + b is y=−32x+0y = -\frac{3}{2}x + 0, which simplifies to y=−32xy = -\frac{3}{2}x.
  4. Write the equation in slope-intercept form: Now we compare the equation y=−32xy = -\frac{3}{2}x with the given options to find the correct one. The correct option is (C) y=−32xy = -\frac{3}{2}x.

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