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What is the slope of the line through (-1,-7) and (3,9) ? Choose 1 answer: (A) -(1)/(4) (B) 4 (c) -4 (D) (1)/(4)

What is the slope of the line through (−1,−7) (-1,-7) and (3,9) (3,9) ?\newlineChoose 11 answer:\newline(A) −14 -\frac{1}{4} \newline(B) 44\newline(C) −4-4\newline(D) 14 \frac{1}{4}

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Q. What is the slope of the line through (−1,−7) (-1,-7) and (3,9) (3,9) ?\newlineChoose 11 answer:\newline(A) −14 -\frac{1}{4} \newline(B) 44\newline(C) −4-4\newline(D) 14 \frac{1}{4}
  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 given points: Substitute the given points into the slope formula.\newlineWe have the points (−1,−7)(-1, -7) and (3,9)(3, 9), so we substitute these into the formula:\newlinex1=−1x_1 = -1, y1=−7y_1 = -7, x2=3x_2 = 3, y2=9y_2 = 9\newlineSlope = 9−(−7)3−(−1)\frac{9 - (-7)}{3 - (-1)}
  3. Calculate change in y: Calculate the change in y (rise). Change in y=y2−y1=9−(−7)=9+7=16y = y_2 - y_1 = 9 - (-7) = 9 + 7 = 16
  4. Calculate change in x: Calculate the change in x (run). Change in x=x2−x1=3−(−1)=3+1=4x = x_2 - x_1 = 3 - (-1) = 3 + 1 = 4
  5. Calculate the slope: Calculate the slope using the changes in yy and xx.Slope=Change in yChange in x=164\text{Slope} = \frac{\text{Change in } y}{\text{Change in } x} = \frac{16}{4}
  6. Simplify the slope: Simplify the slope.\newlineSlope = 164=4\frac{16}{4} = 4

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