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A line that includes the points (6,t)(6,t) and (8,−4)(8,-4) has a slope of 11. What is the value of tt?\newlinet=t = ____

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Full solution

Q. A line that includes the points (6,t)(6,t) and (8,−4)(8,-4) has a slope of 11. What is the value of tt?\newlinet=t = ____
  1. Identify Points and Slope: Identify the points and slope.\newlinePoints: (6,t)(6, t) and (8,−4)(8, -4)\newlineSlope: 11\newlineUse the slope formula: Slope=y2−y1x2−x1\text{Slope} = \frac{y_2 - y_1}{x_2 - x_1}\newline1=−4−t8−61 = \frac{-4 - t}{8 - 6}
  2. Use Slope Formula: Simplify the denominator and solve for tt.1=−4−t21 = \frac{-4 - t}{2}Multiply both sides by 22 to clear the fraction.1×2=−4−t2×21 \times 2 = \frac{-4 - t}{2} \times 22=−4−t2 = -4 - t
  3. Simplify and Solve for tt: Isolate tt.2=−4−t2 = -4 - tAdd 44 to both sides.2+4=−4+4−t2 + 4 = -4 + 4 - t6=−t6 = -tMultiply both sides by −1-1.t=−6t = -6

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