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A line with a slope of −2-2 passes through the points (−4,c)(-4,c) and (−2,−8)(-2,-8). What is the value of cc?\newlinec = ____

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Full solution

Q. A line with a slope of −2-2 passes through the points (−4,c)(-4,c) and (−2,−8)(-2,-8). What is the value of cc?\newlinec = ____
  1. Understand slope formula: Understand 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}\newlineWe know the slope is −2-2, and we have the coordinates of two points (−4,c)(-4, c) and (−2,−8)(-2, -8).
  2. Substitute values into formula: Substitute the known values into the slope formula.\newlineUsing the given slope and points, we have:\newline−2=−8−c−2−(−4)-2 = \frac{-8 - c}{-2 - (-4)}
  3. Simplify denominator of fraction: Simplify the denominator of the fraction.\newline−2=−8−c−2+4-2 = \frac{-8 - c}{-2 + 4}\newline−2=−8−c2-2 = \frac{-8 - c}{2}
  4. Multiply by 22 to solve: Multiply both sides of the equation by 22 to solve for cc.−2×2=(−8−c)-2 \times 2 = (-8 - c)−4=−8−c-4 = -8 - c
  5. Add 88 to isolate c: Add 88 to both sides of the equation to isolate c.\newline−4+8=−8+8−c-4 + 8 = -8 + 8 - c\newline4=−c4 = -c
  6. Multiply both sides by −1-1: Multiply both sides by −1-1 to solve for cc.4×−1=−c×−14 \times -1 = -c \times -1−4=c-4 = c

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