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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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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 slope formula: Identify the slope formula.\newlineThe slope of a line is calculated using the formula: Slope = (change in y)/(change in x)=(y2−y1)/(x2−x1)(\text{change in } y) / (\text{change in } x) = (y_2 - y_1) / (x_2 - x_1).
  2. Substitute given points: Substitute the given points into the slope formula.\newlineWe have the points (−9,6)(-9, 6) and (−3,9)(-3, 9), where x1=−9x_1 = -9, y1=6y_1 = 6, x2=−3x_2 = -3, and y2=9y_2 = 9.\newlineSlope = 9−6−3−(−9)\frac{9 - 6}{-3 - (-9)}
  3. Calculate change in y: Calculate the change in y. Change in y=y2−y1=9−6=3y = y_2 - y_1 = 9 - 6 = 3
  4. Calculate change in x: Calculate the change in x.\newlineChange in x = x2−x1=−3−(−9)=−3+9=6x_2 - x_1 = -3 - (-9) = -3 + 9 = 6
  5. Calculate slope: Calculate the slope using the changes in yy and xx.Slope=Change in yChange in x=36\text{Slope} = \frac{\text{Change in } y}{\text{Change in } x} = \frac{3}{6}
  6. Simplify slope: Simplify the slope to its lowest terms.\newlineSlope = 36=12\frac{3}{6} = \frac{1}{2}
  7. Match to answer choice: Match the calculated slope to the correct answer choice.\newlineThe slope of the line is 12\frac{1}{2}, which corresponds to answer choice (A)(A).

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