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What is the slope of the line through (-9,6) and (-3,9) ? Choose 1 answer: (A) -(1)/(2) (B) -2 (C) (1)/(2) (D) 2

What is the slope of the line through (−9,6)(-9,6) and (−3,9)(-3,9)?\newlineChoose 11 answer:\newline(A) −12-\frac{1}{2}\newline(B) −2-2\newline(C) 12\frac{1}{2}\newline(D) 22

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Full solution

Q. What is the slope of the line through (−9,6)(-9,6) and (−3,9)(-3,9)?\newlineChoose 11 answer:\newline(A) −12-\frac{1}{2}\newline(B) −2-2\newline(C) 12\frac{1}{2}\newline(D) 22
  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 (−3,9)(-3, 9), so x1=−9x_1 = -9, y1=6y_1 = 6, x2=−3x_2 = -3, and y2=9y_2 = 9.\newlineSlope = (9−6)/(−3−(−9))(9 - 6) / (-3 - (-9))
  3. Calculate the change in y: Calculate the change in y y2−y1y_2 - y_1.9−6=39 - 6 = 3
  4. Calculate the change in x: Calculate the change in x x2−x1x_2 - x_1.−3−(−9)=−3+9=6-3 - (-9) = -3 + 9 = 6
  5. Calculate the slope: Calculate the slope using the changes in y and x.\newlineSlope = 36\frac{3}{6}
  6. Simplify the slope: Simplify the slope. 36\frac{3}{6} simplifies to 12\frac{1}{2}

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