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What is the slope of the line through (-4,2) and (3,-3) ? Choose 1 answer: (A) (7)/(5) (B) -(7)/(5) (c) -(5)/(7) (D) (5)/(7)

What is the slope of the line through (−4,2)(-4,2) and (3,−3)(3,-3)? Choose 11 answer: (A) 75\frac{7}{5} (B) −75-\frac{7}{5} (C) −57-\frac{5}{7} (D) 57\frac{5}{7}

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Full solution

Q. What is the slope of the line through (−4,2)(-4,2) and (3,−3)(3,-3)? Choose 11 answer: (A) 75\frac{7}{5} (B) −75-\frac{7}{5} (C) −57-\frac{5}{7} (D) 57\frac{5}{7}
  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 (−4,2)(-4, 2) and (3,−3)(3, -3). Let's denote (−4,2)(-4, 2) as (x1,y1)(x_1, y_1) and (3,−3)(3, -3) as (x2,y2)(x_2, y_2).\newlineSo, x1=−4x_1 = -4, y1=2y_1 = 2, x2=3x_2 = 3, and y2=−3y_2 = -3.\newlineSlope = (3,−3)(3, -3)00
  3. Perform the subtraction: Perform the subtraction in the numerator and the denominator.\newlineNumerator: −3−2=−5-3 - 2 = -5\newlineDenominator: 3−(−4)=3+4=73 - (-4) = 3 + 4 = 7\newlineSlope = −57\frac{-5}{7}
  4. Determine the correct answer: Determine the correct answer from the given options.\newlineThe slope we calculated is −57-\frac{5}{7}, which corresponds to option (C) −(57)-\left(\frac{5}{7}\right).

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