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What is the slope of the line through (1,0) and (3,8) ? Choose 1 answer: (A) -(1)/(4) (B) 4 (C) -4 (D) (1)/(4)

What is the slope of the line through (1,0)(1,0) and (3,8)(3,8)? Choose 11 answer: (A) −14-\frac{1}{4} (B) 44 (C) −4-4 (D) 14\frac{1}{4}

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Full solution

Q. What is the slope of the line through (1,0)(1,0) and (3,8)(3,8)? Choose 11 answer: (A) −14-\frac{1}{4} (B) 44 (C) −4-4 (D) 14\frac{1}{4}
  1. Identify the 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.\newlineSlope formula: y2−y1x2−x1\frac{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 (1,0)(1, 0) and (3,8)(3, 8). Let's assign (x1,y1)=(1,0)(x_1, y_1) = (1, 0) and (x2,y2)=(3,8)(x_2, y_2) = (3, 8).\newlineSlope: (8−0)/(3−1)(8 - 0) / (3 - 1)
  3. Calculate change in y-coordinates: Calculate the change in y-coordinates.\newlineChange in y: 8−0=88 - 0 = 8
  4. Calculate change in x-coordinates: Calculate the change in x-coordinates.\newlineChange in x: 3−1=23 - 1 = 2
  5. Calculate the slope: Calculate the slope using the changes in yy and xx.\newlineSlope: 82\frac{8}{2}
  6. Simplify the fraction: Simplify the fraction to find the slope.\newlineSlope: 82=4\frac{8}{2} = 4

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