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The points (1,−4)(1,-4) and (3,t)(3,t) fall on a line with a slope of 44. What is the value of tt?\newlinet=t = ____

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Full solution

Q. The points (1,−4)(1,-4) and (3,t)(3,t) fall on a line with a slope of 44. What is the value of tt?\newlinet=t = ____
  1. Identify formula for slope: Identify the formula for slope between two points.\newlineThe slope formula is (y2−y1)/(x2−x1)(y_2 - y_1) / (x_2 - x_1). Here, (x1,y1)=(1,−4)(x_1, y_1) = (1, -4) and (x2,y2)=(3,t)(x_2, y_2) = (3, t).
  2. Substitute known values: Substitute the known values into the slope formula.\newlineSlope = 44, so:\newline4=(t−(−4))(3−1)4 = \frac{(t - (-4))}{(3 - 1)}\newline4=(t+4)24 = \frac{(t + 4)}{2}
  3. Solve for t: Solve for t.\newlineMultiply both sides by 22 to clear the fraction:\newline4×2=(t+4)4 \times 2 = (t + 4)\newline8=t+48 = t + 4
  4. Isolate t: Isolate tt. \newlinet=8−4t = 8 - 4\newlinet=5t = 5

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