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What is the slope of the line through (-7,-2) and (-6,7) ? Choose 1 answer: (A) -(1)/(9) (B) -9 (C) (1)/(9) (D) 9

What is the slope of the line through (−7,−2) (-7,-2) and (−6,7) (-6,7) ?\newlineChoose 11 answer:\newline(A) −19 -\frac{1}{9} \newline(B) −9-9\newline(C) 19 \frac{1}{9} \newline(D) 99

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Full solution

Q. What is the slope of the line through (−7,−2) (-7,-2) and (−6,7) (-6,7) ?\newlineChoose 11 answer:\newline(A) −19 -\frac{1}{9} \newline(B) −9-9\newline(C) 19 \frac{1}{9} \newline(D) 99
  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 (−7,−2)(-7, -2) and (−6,7)(-6, 7). Let's denote these points as (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) respectively.\newlineSo, x1=−7x_1 = -7, y1=−2y_1 = -2, x2=−6x_2 = -6, and y2=7y_2 = 7.\newlineSlope = 7−(−2)−6−(−7)\frac{7 - (-2)}{-6 - (-7)}
  3. Calculate change in y: Calculate the change in y y2−y1y_2 - y_1.\newlineChange in y = 7−(−2)=7+2=97 - (-2) = 7 + 2 = 9
  4. Calculate change in x: Calculate the change in xx (x2−x1x_2 - x_1).\newlineChange in x=−6−(−7)=−6+7=1x = -6 - (-7) = -6 + 7 = 1
  5. Calculate slope: Calculate the slope using the changes in yy and xx.Slope=Change in yChange in x=91\text{Slope} = \frac{\text{Change in } y}{\text{Change in } x} = \frac{9}{1}
  6. Simplify slope: Simplify the slope if necessary.\newlineThe slope simplifies to 91\frac{9}{1}, which is an integer value of 99.

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