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A line that includes the points (−5,r)(-5,r) and (−4,8)(-4,8) has a slope of 66. What is the value of rr?\newliner = ____

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Full solution

Q. A line that includes the points (−5,r)(-5,r) and (−4,8)(-4,8) has a slope of 66. What is the value of rr?\newliner = ____
  1. Given Points and Slope: We are given two points: (−5,r)(-5, r) and (−4,8)(-4, 8), and the slope of the line is 66. We will use the slope formula to find the value of rr.\newlineSlope mm = y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}\newline6=8−r−4−(−5)6 = \frac{8 - r}{-4 - (-5)}
  2. Calculate Slope: Now we simplify the denominator of the slope equation.\newline6=8−r−4+56 = \frac{8 - r}{-4 + 5}\newline6=8−r16 = \frac{8 - r}{1}
  3. Simplify Equation: Since the denominator is 11, we can multiply both sides of the equation by 11 to isolate the numerator.\newline6×1=(8−r)×16 \times 1 = (8 - r) \times 1\newline6=8−r6 = 8 - r
  4. Isolate Numerator: Now we solve for rr by moving the terms around.6=8−r6 = 8 - r6−8=−r6 - 8 = -r−2=−r-2 = -r
  5. Solve for rr: To find rr, we multiply both sides by −1-1.r=2r = 2

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