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A line that includes the points (−8,t)(-8,t) and (1,−4)(1,-4) has a slope of −1-1. What is the value of tt?\newlinet = ____

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Full solution

Q. A line that includes the points (−8,t)(-8,t) and (1,−4)(1,-4) has a slope of −1-1. What is the value of tt?\newlinet = ____
  1. Identify Slope Formula: To find the value of tt, we need to use the slope formula, which is y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}. We know the slope (mm) is −1-1, and we have the points (−8,t)(-8, t) and (1,−4)(1, -4). Let's denote (−8,t)(-8, t) as (x1,y1)(x_1, y_1) and (1,−4)(1, -4) as (x2,y2)(x_2, y_2).
  2. Calculate Slope Using Points: Using the slope formula with our points, we get:\newlinem=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}\newline−1=−4−t1−(−8)-1 = \frac{-4 - t}{1 - (-8)}
  3. Simplify Denominator: Now we simplify the denominator of the fraction:\newline−1=−4−t1+8-1 = \frac{-4 - t}{1 + 8}\newline−1=−4−t9-1 = \frac{-4 - t}{9}
  4. Multiply by 99: Next, we multiply both sides of the equation by 99 to solve for tt:inlinelatex1inline_latex_1inlinelatex2inline_latex_2
  5. Isolate tt: Now we add 44 to both sides of the equation to isolate tt:−9+4=−4+4−t-9 + 4 = -4 + 4 - t−5=−t-5 = -t
  6. Finalize Solution: Finally, we multiply both sides by −1-1 to solve for tt:−1×−5=−1×−t-1 \times -5 = -1 \times -t5=t5 = t

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