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A line has a slope of −8-8 and includes the points (−3,−6)(-3,-6) and (−5,t)(-5,t). What is the value of tt?\newlinet = ____

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Full solution

Q. A line has a slope of −8-8 and includes the points (−3,−6)(-3,-6) and (−5,t)(-5,t). What is the value of tt?\newlinet = ____
  1. Identify Given Points and Slope: Identify the given points and the slope.\newlineWe have the points (−3,−6)(-3, -6) and (−5,t)(-5, t) with a slope of −8-8.\newlineWe will use the slope formula which is (y2−y1)/(x2−x1)=slope.(y_2 - y_1) / (x_2 - x_1) = \text{slope}.
  2. Plug Values into Formula: Plug the values into the slope formula.\newlineUsing the slope formula, we have:\newline−8=t−(−6)−5−(−3)-8 = \frac{t - (-6)}{-5 - (-3)}
  3. Simplify Equation: Simplify the equation.\newline−8=t+6−5+3-8 = \frac{t + 6}{-5 + 3}\newline−8=t+6−2-8 = \frac{t + 6}{-2}
  4. Multiply to Isolate tt: Multiply both sides by −2-2 to isolate tt.\newline−8×(−2)=t+6−2×(−2)-8 \times (-2) = \frac{t + 6}{-2} \times (-2)\newline16=t+616 = t + 6
  5. Subtract to Solve for tt: Subtract 66 from both sides to solve for tt.16−6=t+6−616 - 6 = t + 6 - 610=t10 = t

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