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A line has a slope of −1-1 and includes the points (8,r)(8,r) and (10,−8)(10,-8). What is the value of rr?\newliner=r = ____

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Full solution

Q. A line has a slope of −1-1 and includes the points (8,r)(8,r) and (10,−8)(10,-8). What is the value of rr?\newliner=r = ____
  1. Write Slope Formula: We know the formula for the slope between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}. Here, the slope is given as −1-1, and the points are (8,r)(8, r) and (10,−8)(10, -8).
  2. Substitute Values: Substitute the values into the slope formula: \newlineSlope = −8−r10−8\frac{-8 - r}{10 - 8} \newline−1=−8−r2-1 = \frac{-8 - r}{2}
  3. Eliminate Denominator: Multiply both sides by 22 to eliminate the denominator:\newline−1×2=−8−r(-1 \times 2 = -8 - r (\newline-2 = -8 - r\)
  4. Solve for r: Add 88 to both sides to solve for rr: \newline−2+8=−8−r+8-2 + 8 = -8 - r + 8\newline6=−r6 = -r
  5. Final Solution: Multiply both sides by −1-1 to solve for rr:6×−1=−r×−16 \times -1 = -r \times -1 −6=r-6 = r

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