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A line that includes the points (9,t)(9,t) and (10,−10)(10,-10) has a slope of −8-8. What is the value of tt?\newlinet = ____

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Full solution

Q. A line that includes the points (9,t)(9,t) and (10,−10)(10,-10) has a slope of −8-8. What is the value of tt?\newlinet = ____
  1. Calculate Slope Formula: The slope of a line is calculated using the formula (change in y)/(change in x)(\text{change in } y) / (\text{change in } x), which is also known as rise over run. We can use the coordinates of the two points (9,t)(9,t) and (10,−10)(10,-10) to find the value of tt.
  2. Substitute Coordinates: The slope formula is (y2−y1)/(x2−x1)(y_2 - y_1) / (x_2 - x_1). We know the slope is −8-8, x1x_1 is 99, y1y_1 is tt, x2x_2 is 1010, and y2y_2 is −10-10. Plugging these values into the slope formula gives us:\newline−8-800
  3. Simplify Equation: Simplify the denominator 10−910 - 9 to get 11, so the equation becomes: −10−t=−8×1-10 - t = -8 \times 1
  4. Add 1010 to Both Sides: Now, we solve for tt by adding 1010 to both sides of the equation:\newline−10−t+10=−8+10-10 - t + 10 = -8 + 10
  5. Solve for t: This simplifies to: −t=2-t = 2
  6. Solve for t: This simplifies to:\newline−t=2-t = 2 To find the value of t, we multiply both sides by −1-1:\newlinet=−2t = -2

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