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A line with a slope of 77 passes through the points (2,−5)(2,-5) and (4,t)(4,t). What is the value of tt?\newlinet = ____

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Q. A line with a slope of 77 passes through the points (2,−5)(2,-5) and (4,t)(4,t). What is the value of tt?\newlinet = ____
  1. Understand slope concept: Understand the concept of slope.\newlineThe slope of a line is the ratio of the change in the yy-coordinate to the change in the xx-coordinate between two points on the line. The formula for slope (mm) is given by:\newlinem=(y2−y1)(x2−x1)m = \frac{(y_2 - y_1)}{(x_2 - x_1)}\newlineHere, we are given the slope (mm) as 77, and we have the coordinates of two points on the line: (2,−5)(2, -5) and (4,t)(4, t).
  2. Plug values into formula: Plug the known values into the slope formula.\newlineWe can use the given slope and the coordinates of the two points to create an equation:\newline7=t−(−5)4−27 = \frac{t - (-5)}{4 - 2}
  3. Simplify equation: Simplify the equation.\newline7=t+54−27 = \frac{t + 5}{4 - 2}\newline7=t+527 = \frac{t + 5}{2}
  4. Solve for t: Solve for t.\newlineTo find tt, we need to multiply both sides of the equation by 22:\newline2×7=t+52 \times 7 = t + 5\newline14=t+514 = t + 5
  5. Subtract to isolate tt: Subtract 55 from both sides to isolate tt.14−5=t14 - 5 = t9=t9 = t

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