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The points (−8,c)(-8,c) and (−10,−4)(-10,-4) fall on a line with a slope of 77. What is the value of cc?\newlinec=___c = \_\_\_

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Q. The points (−8,c)(-8,c) and (−10,−4)(-10,-4) fall on a line with a slope of 77. What is the value of cc?\newlinec=___c = \_\_\_
  1. Identify Given Points and Slope: Identify the given points and the slope.\newlineWe have the points (−8-8, c) and (−10-10, −4-4) with a slope of 77.\newlineThe formula for the slope (m) between two points (x11, y11) and (x22, y22) is given by:\newlinem=y2−y1x2−x1 m = \frac{y2 - y1}{x2 - x1}
  2. Plug Values into Formula: Plug the given values into the slope formula.\newlineUsing the slope formula, we have:\newline7=−4−c−10−(−8) 7 = \frac{-4 - c}{-10 - (-8)}
  3. Simplify Denominator: Simplify the denominator of the slope equation.\newline7=−4−c−10+8 7 = \frac{-4 - c}{-10 + 8} \newline7=−4−c−2 7 = \frac{-4 - c}{-2}
  4. Multiply by −2-2: Multiply both sides of the equation by −2-2 to solve for c.\newline7×(−2)=(−4−c) 7 \times (-2) = (-4 - c) \newline−14=−4−c -14 = -4 - c
  5. Add 44 to Isolate c: Add 44 to both sides of the equation to isolate c.\newline−14+4=−4+4−c -14 + 4 = -4 + 4 - c \newline−10=−c -10 = -c
  6. Multiply by −1-1: Multiply both sides by −1-1 to solve for c.\newline−10×(−1)=−c×(−1) -10 \times (-1) = -c \times (-1) \newline10=c 10 = c

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