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A line has a slope of 99 and includes the points (−2,t)(-2,t) and (−1,2)(-1,2). What is the value of tt?\newlinet = ____

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Full solution

Q. A line has a slope of 99 and includes the points (−2,t)(-2,t) and (−1,2)(-1,2). What is the value of tt?\newlinet = ____
  1. Use Slope Formula: To find the value of tt, we can use the slope formula, which is (change in y)/(change in x)=slope(\text{change in } y) / (\text{change in } x) = \text{slope}. Here, we have two points (−2,t)(-2, t) and (−1,2)(-1, 2), and the slope is given as 99.
  2. Calculate Change in y and x: The change in yy is (t−2)(t - 2), and the change in xx is (−2−(−1))(-2 - (-1)) or (−2+1)(-2 + 1), which simplifies to −1-1. So, the slope formula with our values is t−2−1=9\frac{t - 2}{-1} = 9.
  3. Apply Slope Formula: To find tt, we multiply both sides of the equation by −1-1 to get rid of the denominator. This gives us t−2=−9t - 2 = -9.
  4. Solve for t: Now, we add 22 to both sides of the equation to solve for tt. This gives us t=−9+2t = -9 + 2.
  5. Final Calculation: Calculating t=−9+2t = -9 + 2 gives us t=−7t = -7.

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