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What is the slope of the line through (2,-2) and (9,3) ? Choose 1 answer: (A) (7)/(5) (B) (5)/(7) (C) -(7)/(5) (D) -(5)/(7)

What is the slope of the line through (2,−2) (2,-2) and (9,3) (9,3) ?\newlineChoose 11 answer:\newline(A) 75 \frac{7}{5} \newline(B) 57 \frac{5}{7} \newline(c) −75 -\frac{7}{5} \newline(D) −57 -\frac{5}{7}

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Full solution

Q. What is the slope of the line through (2,−2) (2,-2) and (9,3) (9,3) ?\newlineChoose 11 answer:\newline(A) 75 \frac{7}{5} \newline(B) 57 \frac{5}{7} \newline(c) −75 -\frac{7}{5} \newline(D) −57 -\frac{5}{7}
  1. Identify 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 given points: Substitute the given points into the slope formula.\newlineWe have the points (2,−2)(2, -2) and (9,3)(9, 3), so x1=2x_1 = 2, y1=−2y_1 = -2, x2=9x_2 = 9, and y2=3y_2 = 3.\newlineSlope = (3−(−2))/(9−2)(3 - (-2)) / (9 - 2)
  3. Calculate change in y: Calculate the change in y y2−y1y_2 - y_1.\newlineChange in y = 3−(−2)=3+2=53 - (-2) = 3 + 2 = 5
  4. Calculate change in x: Calculate the change in x x2−x1x_2 - x_1.\newlineChange in x = 9−2=79 - 2 = 7
  5. Calculate slope: Calculate the slope using the changes in yy and xx.Slope=Change in yChange in x=57\text{Slope} = \frac{\text{Change in } y}{\text{Change in } x} = \frac{5}{7}
  6. Match calculated slope: Match the calculated slope to the given answer choices.\newlineThe calculated slope is 57\frac{5}{7}, which corresponds to answer choice (B)(B).

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