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What is the slope of the line through (-10,1) and (0,-4) ? Choose 1 answer: (A) 2 (B) (1)/(2) (C) -(1)/(2) (D) -2

What is the slope of the line through (−10,1)(-10,1) and (0,−4)(0,-4)? Choose 11 answer: \newline(A) 22 \newline(B) 12\frac{1}{2} \newline(C) −12-\frac{1}{2} \newline(D) −2-2

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Full solution

Q. What is the slope of the line through (−10,1)(-10,1) and (0,−4)(0,-4)? Choose 11 answer: \newline(A) 22 \newline(B) 12\frac{1}{2} \newline(C) −12-\frac{1}{2} \newline(D) −2-2
  1. Identify the slope formula: Identify the slope formula.\newlineThe slope of a line passing 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 the given points: Substitute the given points into the slope formula.\newlineWe have the points (−10,1)(-10, 1) and (0,−4)(0, -4). Let's denote these points as (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) respectively.\newlineSo, x1=−10x_1 = -10, y1=1y_1 = 1, x2=0x_2 = 0, and y2=−4y_2 = -4.\newlineSlope = y2−y1x2−x1=−4−10−(−10)\frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - 1}{0 - (-10)}
  3. Calculate the change in y: Calculate the change in y y2−y1y_2 - y_1.\newlineChange in y = −4−1=−5-4 - 1 = -5
  4. Calculate the change in x: Calculate the change in x (x2−x1)(x_2 - x_1).\newlineChange in x = 0−(−10)=0+10=100 - (-10) = 0 + 10 = 10
  5. Calculate the slope: Calculate the slope using the changes in y and x.\newlineSlope = Change in yChange in x=−510 \frac{\text{Change in } y}{\text{Change in } x} = \frac{-5}{10}
  6. Simplify the slope: Simplify the slope to its lowest terms.\newlineSlope = −510=−12\frac{-5}{10} = \frac{-1}{2}
  7. Match the calculated slope: Match the calculated slope to the given answer choices.\newlineThe calculated slope is −12-\frac{1}{2}, which corresponds to answer choice (C) −(12)-\left(\frac{1}{2}\right).

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