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What is the slope of the line through (-4,2) and (3,-3) ? Choose 1 answer: (A) (7)/(5) (B) -(5)/(7) (C) (5)/(7) (D) -(7)/(5)

What is the slope of the line through (−4,2) (-4,2) and (3,−3) (3,-3) ?\newlineChoose 11 answer:\newline(A) 75 \frac{7}{5} \newline(B) −57 -\frac{5}{7} \newline(C) 57 \frac{5}{7} \newline(D) −75 -\frac{7}{5}

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Full solution

Q. What is the slope of the line through (−4,2) (-4,2) and (3,−3) (3,-3) ?\newlineChoose 11 answer:\newline(A) 75 \frac{7}{5} \newline(B) −57 -\frac{5}{7} \newline(C) 57 \frac{5}{7} \newline(D) −75 -\frac{7}{5}
  1. Identify slope formula: Identify the slope formula.\newlineThe slope of a line is calculated by the difference in the yy-coordinates divided by the difference in the xx-coordinates of two points on the line.\newlineSlope formula: (y2−y1)/(x2−x1)(y_2 - y_1)/(x_2 - x_1)
  2. Substitute given points: Substitute the given points into the slope formula.\newlineWe have the points (−4,2)(-4, 2) and (3,−3)(3, -3). Let's denote (−4,2)(-4, 2) as (x1,y1)(x_1, y_1) and (3,−3)(3, -3) as (x2,y2)(x_2, y_2).\newlineSlope: −3−23−(−4)\frac{-3 - 2}{3 - (-4)}
  3. Calculate change in y: Calculate the change in y y2−y1y_2 - y_1.−3−2-3 - 2 equals −5-5.
  4. Calculate change in x: Calculate the change in xx (x2−x1x_2 - x_1).\newline3−(−4)3 - (-4) equals 77.
  5. Calculate slope: Calculate the slope using the changes in yy and xx.Slope=−57\text{Slope} = \frac{-5}{7}
  6. Simplify slope: Simplify the slope if necessary.\newlineThe slope −57-\frac{5}{7} is already in simplest form and matches one of the given answer choices.

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