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A line that includes the points (10,1)(10,1) and (9,t)(9,t) has a slope of 88. What is the value of tt?\newlinet = ____

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Full solution

Q. A line that includes the points (10,1)(10,1) and (9,t)(9,t) has a slope of 88. What is the value of tt?\newlinet = ____
  1. Understand the formula: Understand the formula for the slope of a line.\newlineThe slope of a line is calculated by the difference in the yy-coordinates divided by the difference in the xx-coordinates between two points on the line. The formula is:\newlineslope (mm) = (y2−y1)/(x2−x1)(y_2 - y_1) / (x_2 - x_1)
  2. Apply the formula: Apply the slope formula to the given points and slope.\newlineWe have the points (10,1)(10,1) and (9,t)(9,t) and a slope of 88. Let's denote (10,1)(10,1) as (x1,y1)(x_1, y_1) and (9,t)(9,t) as (x2,y2)(x_2, y_2). According to the slope formula:\newline8=t−19−108 = \frac{t - 1}{9 - 10}
  3. Simplify and solve: Simplify the denominator and solve for tt. The denominator 9−109 - 10 simplifies to −1-1. So we have: 8=t−1−18 = \frac{t - 1}{-1} To solve for tt, we multiply both sides by −1-1: 8×(−1)=t−18 \times (-1) = t - 1 −8=t−1-8 = t - 1
  4. Isolate tt: Add 11 to both sides to isolate tt.\newline−8+1=t−1+1-8 + 1 = t - 1 + 1\newline−7=t-7 = t

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