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A line that includes the points (7,t)(7,t) and (8,7)(8,7) has a slope of 55. What is the value of tt?\newlinet = ____

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Full solution

Q. A line that includes the points (7,t)(7,t) and (8,7)(8,7) has a slope of 55. What is the value of tt?\newlinet = ____
  1. Understand slope formula: Understand the formula for the slope of a line. The slope of a line is calculated by the change in yy divided by the change in xx (rise over run). The formula for the slope (mm) between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}
  2. Apply formula to given points: Apply the slope formula to the given points and slope.\newlineWe know the slope mm is 55, and we have the points (7,t)(7, t) and (8,7)(8, 7). Let's plug these into the slope formula:\newline5=7−t8−75 = \frac{7 - t}{8 - 7}
  3. Simplify denominator and solve: Simplify the denominator and solve for tt. Since 8−7=18 - 7 = 1, the equation simplifies to: 5=7−t5 = 7 - t Now, we solve for tt by subtracting 77 from both sides: 5−7=−t5 - 7 = -t −2=−t-2 = -t To find tt, we multiply both sides by −1-1: t=2t = 2

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