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What is the slope of the line through (-9,6) and (-6,-9) ? Choose 1 answer: (A) (1)/(5) (B) -(1)/(5) (c) 5 (D) -5

What is the slope of the line through (−9,6)(-9,6) and (−6,−9)(-6,-9)? Choose 11 answer: \newline(A) 15\frac{1}{5} \newline(B) −15-\frac{1}{5} \newline(C) 55 \newline(D) −5-5

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Full solution

Q. What is the slope of the line through (−9,6)(-9,6) and (−6,−9)(-6,-9)? Choose 11 answer: \newline(A) 15\frac{1}{5} \newline(B) −15-\frac{1}{5} \newline(C) 55 \newline(D) −5-5
  1. Identify the slope formula: Identify the slope formula.\newlineThe slope of a line through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by the formula:\newlineSlope = y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}
  2. Substitute the given points: Substitute the given points into the slope formula.\newlineWe have the points (−9,6)(-9, 6) and (−6,−9)(-6, -9), so we assign x1=−9x_1 = -9, y1=6y_1 = 6, x2=−6x_2 = -6, and y2=−9y_2 = -9.\newlineSlope = −9−6−6−(−9)\frac{-9 - 6}{-6 - (-9)}
  3. Calculate the change in y: Calculate the change in y y2−y1y_2 - y_1.\newlineChange in y = −9−6=−15-9 - 6 = -15
  4. Calculate the change in x: Calculate the change in x (x2−x1)(x_2 - x_1).\newlineChange in x = −6−(−9)=−6+9=3-6 - (-9) = -6 + 9 = 3
  5. Calculate the slope: Calculate the slope using the changes in y and x.\newlineSlope = −153=−5\frac{-15}{3} = -5
  6. Match the calculated slope: Match the calculated slope to the given answer choices.\newlineThe calculated slope is −5-5, which corresponds to answer choice (D) −5-5.

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