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A line that includes the points (−8,h)(-8,h) and (−9,−9)(-9,-9) has a slope of 55. What is the value of hh?\newlineh = ____

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Full solution

Q. A line that includes the points (−8,h)(-8,h) and (−9,−9)(-9,-9) has a slope of 55. What is the value of hh?\newlineh = ____
  1. Calculate Slope Formula: To find the value of hh, we need to use the formula for the slope of a line, which is (change in yy) / (change in xx). The slope is given as 55, and we have the coordinates of two points on the line: (−8,h)(-8, h) and (−9,−9)(-9, -9).\newlineThe formula for the slope (mm) is:\newlinem=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}\newlineHere, (x1,y1)=(−8,h)(x1, y1) = (-8, h) and (x2,y2)=(−9,−9)(x2, y2) = (-9, -9).
  2. Substitute Values: Substitute the known values into the slope formula:\newline5=(−9−h)/(−9−(−8))5 = (-9 - h) / (-9 - (-8))\newline5=(−9−h)/(−9+8)5 = (-9 - h) / (-9 + 8)\newline5=(−9−h)/(−1)5 = (-9 - h) / (-1)
  3. Solve for h: To find the value of h, we need to solve for h. We can start by multiplying both sides of the equation by −1-1 to get rid of the negative denominator:\newline5×(−1)=(−9−h)5 \times (-1) = (-9 - h)\newline−5=−9−h-5 = -9 - h
  4. Isolate h: Now, we add 99 to both sides of the equation to isolate hh: \newline−5+9=−9−h+9-5 + 9 = -9 - h + 9\newline4=−h4 = -h
  5. Final Solution for h: Finally, we multiply both sides by −1-1 to solve for h:\newline4×(−1)=−h×(−1)4 \times (-1) = -h \times (-1)\newline−4=h-4 = h

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