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What is the slope of the line through (1,-1) and (5,-7) ? Choose 1 answer: (A) -(3)/(2) (B) (3)/(2) (c) -(2)/(3) (D) (2)/(3)

What is the slope of the line through (1,−1)(1,-1) and (5,−7)(5,-7)? Choose 11 answer: (A) −32-\frac{3}{2} (B) 32\frac{3}{2} (C) −23-\frac{2}{3} (D) 23\frac{2}{3}

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Full solution

Q. What is the slope of the line through (1,−1)(1,-1) and (5,−7)(5,-7)? Choose 11 answer: (A) −32-\frac{3}{2} (B) 32\frac{3}{2} (C) −23-\frac{2}{3} (D) 23\frac{2}{3}
  1. Identify the slope formula: Identify the slope formula.\newlineThe slope of a line is calculated by the change in y-coordinates divided by the change in x-coordinates between two points on the line.\newlineSlope formula: (y2−y1)/(x2−x1)(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 (1,−1)(1, -1) and (5,−7)(5, -7). Let's denote (1,−1)(1, -1) as (x1,y1)(x_1, y_1) and (5,−7)(5, -7) as (x2,y2)(x_2, y_2).\newlineSlope: −7−(−1)5−1\frac{-7 - (-1)}{5 - 1}
  3. Calculate change in y-coordinates: Calculate the change in y-coordinates.\newlineChange in y: −7−(−1)-7 - (-1) which simplifies to −7+1-7 + 1 which equals −6-6.
  4. Calculate change in x-coordinates: Calculate the change in x-coordinates.\newlineChange in x: 5−15 - 1 which equals 44.
  5. Calculate the slope: Calculate the slope using the changes in y and x.\newlineSlope: (−6)/4(-6) / 4 which simplifies to −3/2-3/2 or −(32)-\left(\frac{3}{2}\right).

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