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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) ?\newlineChoose 11 answer:\newline(A) 32 \frac{3}{2} \newline(B) −32 -\frac{3}{2} \newline(C) −23 -\frac{2}{3} \newline(D) 23 \frac{2}{3}

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Q. What is the slope of the line through (1,−1) (1,-1) and (5,−7) (5,-7) ?\newlineChoose 11 answer:\newline(A) 32 \frac{3}{2} \newline(B) −32 -\frac{3}{2} \newline(C) −23 -\frac{2}{3} \newline(D) 23 \frac{2}{3}
  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 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 assign these values to the formula:\newlinex1=1x_1 = 1, y1=−1y_1 = -1, x2=5x_2 = 5, y2=−7y_2 = -7\newlineSlope = y2−y1x2−x1=−7−(−1)5−1\frac{y_2 - y_1}{x_2 - x_1} = \frac{-7 - (-1)}{5 - 1}
  3. Perform subtraction: Perform the subtraction in the numerator and the denominator.\newlineCalculate the change in yy (y2−y1y_2 - y_1):\newline−7−(−1)=−7+1=−6-7 - (-1) = -7 + 1 = -6\newlineCalculate the change in xx (x2−x1x_2 - x_1):\newline5−1=45 - 1 = 4\newlineNow we have:\newlineSlope = −64\frac{-6}{4}
  4. Simplify the fraction: Simplify the fraction.\newlineSlope = (−6)/(4)(-6) / (4) can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 22.\newlineSlope = (−6÷2)/(4÷2)=−3/2(-6 \div 2) / (4 \div 2) = -3 / 2

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