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A line has a slope of 55 and includes the points (7,−2)(7,-2) and (8,d)(8,d). What is the value of dd?\newlined = ____

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Q. A line has a slope of 55 and includes the points (7,−2)(7,-2) and (8,d)(8,d). What is the value of dd?\newlined = ____
  1. Identify Points and Slope: Identify the given points and the slope.\newlineWe have the points (7,−2)(7, -2) and (8,d)(8, d) and the slope of the line is 55.
  2. Use Slope Formula: Use the slope formula to set up an equation.\newlineThe slope formula is (y2−y1)/(x2−x1)=slope(y_2 - y_1) / (x_2 - x_1) = \text{slope}. Here, (x1,y1)=(7,−2)(x_1, y_1) = (7, -2) and (x2,y2)=(8,d)(x_2, y_2) = (8, d), and the slope is 55.\newlineSo, (d−(−2))/(8−7)=5(d - (-2)) / (8 - 7) = 5.
  3. Simplify Equation: Simplify the equation and solve for dd.(d+2)/(1)=5.(d + 2) / (1) = 5.This simplifies to d+2=5d + 2 = 5.
  4. Find Value of d: Subtract 22 from both sides to find the value of dd.\newlined+2−2=5−2.d + 2 - 2 = 5 - 2.\newlined=3.d = 3.

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