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

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

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Q. What is the slope of the line through (−2,−6)(-2,-6) and (2,2)(2,2)?\newlineChoose 11 answer:\newline(A) 12\frac{1}{2}\newline(B) −2-2\newline(C) 22\newline(D) −12-\frac{1}{2}
  1. Identify slope formula: Identify the slope formula.\newlineThe slope of a line is calculated by the change in yy-coordinates divided by the change in xx-coordinates between two points.\newlineSlope formula: (y2−y1)/(x2−x1)(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,−6)(-2, -6) and (2,2)(2, 2). Let's denote (−2,−6)(-2, -6) as (x1,y1)(x_1, y_1) and (2,2)(2, 2) as (x2,y2)(x_2, y_2).\newlineSlope: (2−(−6))/(2−(−2))(2 - (-6)) / (2 - (-2))
  3. Calculate change in y-coordinates: Calculate the change in y-coordinates.\newlineChange in y: 2−(−6)2 - (-6) which simplifies to 2+6=82 + 6 = 8
  4. Calculate change in x-coordinates: Calculate the change in x-coordinates.\newlineChange in x: 2−(−2)2 - (-2) which simplifies to 2+2=42 + 2 = 4
  5. Calculate slope using changes in y and x: Calculate the slope using the changes in y and x.\newlineSlope: 84\frac{8}{4}
  6. Simplify fraction to find slope: Simplify the fraction to find the slope. 84\frac{8}{4} simplifies to 22
  7. Match calculated slope to answer choice: Match the calculated slope to the correct answer choice.\newlineThe calculated slope is 22, which corresponds to answer choice (C) 22.

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