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The points (7,−9)(7,-9) and (6,c)(6,c) fall on a line with a slope of −5-5. What is the value of cc?\newlinec = ____

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Full solution

Q. The points (7,−9)(7,-9) and (6,c)(6,c) fall on a line with a slope of −5-5. What is the value of cc?\newlinec = ____
  1. Identify Points and Slope: Identify the given points and the slope.\newlineWe have the points (7,−9)(7, -9) and (6,c)(6, c) and the slope of the line is −5-5.
  2. Use Slope Formula: Use the slope formula to set up an equation.\newlineThe slope formula is (y2−y1)/(x2−x1)(y_2 - y_1) / (x_2 - x_1). Let's plug in our values.\newline−5=(c−(−9))/(6−7)-5 = (c - (-9)) / (6 - 7)
  3. Simplify Equation: Simplify the equation.\newline−5=c+96−7-5 = \frac{c + 9}{6 - 7}\newline−5=c+9−1-5 = \frac{c + 9}{-1}
  4. Isolate c: Multiply both sides by −1-1 to isolate cc.−5×−1=c+9−1×−1-5 \times -1 = \frac{c + 9}{-1} \times -15=c+95 = c + 9
  5. Solve for c: Solve for c.\newline5=c+95 = c + 9\newline5−9=c5 - 9 = c\newlinec=−4c = -4

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