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The points (8,r)(8,r) and (7,−1)(7,-1) fall on a line with a slope of −7-7. What is the value of rr?\newliner = ____

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Full solution

Q. The points (8,r)(8,r) and (7,−1)(7,-1) fall on a line with a slope of −7-7. What is the value of rr?\newliner = ____
  1. Understand slope concept: Understand the concept of slope. The slope of a line is the ratio of the change in the yy-coordinates to the change in the xx-coordinates between two points on the line. The formula for slope (mm) is given by: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}
  2. Apply slope formula: Apply the slope formula to the given points and slope.\newlineWe are given the slope m=−7m = -7, and two points (8,r)(8, r) and (7,−1)(7, -1). Let's plug these values into the slope formula:\newline−7=r−(−1)8−7-7 = \frac{r - (-1)}{8 - 7}
  3. Simplify and solve for rr: Simplify the equation and solve for rr.−7=(r+1)1-7 = \frac{(r + 1)}{1} Now, multiply both sides by 11 to isolate (r+1)(r + 1) on one side:−7×1=r+1-7 \times 1 = r + 1
  4. Subtract to find rr: Subtract 11 from both sides to solve for rr.\newline−7−1=r-7 - 1 = r\newliner=−8r = -8

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