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A line has a slope of 77 and includes the points (6,4)(6,4) and (5,r)(5,r). What is the value of rr?\newliner=___r = \_\_\_

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Q. A line has a slope of 77 and includes the points (6,4)(6,4) and (5,r)(5,r). What is the value of rr?\newliner=___r = \_\_\_
  1. Set up slope equation: Points: (6,4)(6, 4) and (5,r)(5, r)\newlineSlope: 77\newlineUse the slope formula to set up the equation.\newlineSlope =y2−y1x2−x1= \frac{y_2 - y_1}{x_2 - x_1}\newline7=r−45−67 = \frac{r - 4}{5 - 6}
  2. Simplify denominator: 7=r−45−67 = \frac{r - 4}{5 - 6}\newlineSimplify the denominator.\newline7=r−4−17 = \frac{r - 4}{-1}
  3. Isolate (r−4)(r - 4): 7=(r−4)(−1)7 = \frac{(r - 4)}{(-1)}\newlineMultiply both sides by −1-1 to isolate (r−4)(r - 4).\newline7×(−1)=(r−4)(−1)×(−1)7 \times (-1) = \frac{(r - 4)}{(-1)} \times (-1)\newline−7=r−4-7 = r - 4
  4. Solve for rr: −7=r−4-7 = r - 4\newlineAdd 44 to both sides to solve for rr.\newline−7+4=r−4+4-7 + 4 = r - 4 + 4\newline−3=r-3 = r

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