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What is the slope of the line through (-1,8) and (3,-4) ? Choose 1 answer: (A) -(1)/(3) (B) (1)/(3) (c) 3 (D) -3

What is the slope of the line through (−1,8)(-1,8) and (3,−4)(3,-4)? Choose 11 answer: \newline(A) −13-\frac{1}{3} \newline(B) 13\frac{1}{3} \newline(C) 33 \newline(D) −3-3

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Full solution

Q. What is the slope of the line through (−1,8)(-1,8) and (3,−4)(3,-4)? Choose 11 answer: \newline(A) −13-\frac{1}{3} \newline(B) 13\frac{1}{3} \newline(C) 33 \newline(D) −3-3
  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 (−1,8)(-1, 8) and (3,−4)(3, -4), so x1=−1x_1 = -1, y1=8y_1 = 8, x2=3x_2 = 3, and y2=−4y_2 = -4.\newlineSlope =(−4−8)(3−(−1))= \frac{(-4 - 8)}{(3 - (-1))}
  3. Calculate the change in y: Calculate the change in y y2−y1y_2 - y_1.\newlineChange in y = −4−8=−12-4 - 8 = -12
  4. Calculate the change in x: Calculate the change in x (x2−x1)(x_2 - x_1).\newlineChange in x = 3−(−1)=3+1=43 - (-1) = 3 + 1 = 4
  5. Calculate the slope: Calculate the slope using the changes in y and x.\newlineSlope = −124\frac{-12}{4} = −3-3
  6. Match the calculated slope: Match the calculated slope to the given answer choices.\newlineThe calculated slope is −3-3, which corresponds to answer choice (D).

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