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What is the slope of the line through (-9,-6) and (3,-9) ? Choose 1 answer: (A) -4 (B) (1)/(4) (c) 4 (D) -(1)/(4)

What is the slope of the line through (−9,−6)(-9,-6) and (3,−9)(3,-9)? Choose 11 answer: \newline(A) −4-4 \newline(B) 14\frac{1}{4} \newline(C) 44 \newline(D) −14-\frac{1}{4}

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Full solution

Q. What is the slope of the line through (−9,−6)(-9,-6) and (3,−9)(3,-9)? Choose 11 answer: \newline(A) −4-4 \newline(B) 14\frac{1}{4} \newline(C) 44 \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 the given points: Substitute the given points into the slope formula.\newlineWe have the points (−9,−6)(-9, -6) and (3,−9)(3, -9). Let's assign these values to the formula:\newlinex1=−9x_1 = -9, y1=−6y_1 = -6, x2=3x_2 = 3, y2=−9y_2 = -9.\newlineSlope = −9−(−6)3−(−9)\frac{-9 - (-6)}{3 - (-9)}
  3. Simplify the numerator and denominator: Simplify the numerator and the denominator.\newlineSimplify the numerator: −9−(−6)=−9+6=−3-9 - (-6) = -9 + 6 = -3\newlineSimplify the denominator: 3−(−9)=3+9=123 - (-9) = 3 + 9 = 12\newlineSlope = −312-\frac{3}{12}
  4. Reduce the fraction to simplest form: Reduce the fraction to its simplest form.\newline−312-\frac{3}{12} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 33.\newlineSlope = (−33)/(123)=−14\left(-\frac{3}{3}\right) / \left(\frac{12}{3}\right) = -\frac{1}{4}
  5. Choose the correct answer: Choose the correct answer from the given options.\newlineThe simplified slope is −14-\frac{1}{4}, which corresponds to option (D).

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