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A line with a slope of 55 passes through the points (−7,−6)(-7,-6) and (−6,t)(-6,t). What is the value of tt?\newlinet = ____

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Full solution

Q. A line with a slope of 55 passes through the points (−7,−6)(-7,-6) and (−6,t)(-6,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 any two points on the line. It is often represented by the letter 'mm'.\newlineThe formula for slope when given two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is:\newlinem=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}
  2. Apply slope formula: Apply the slope formula to the given points and slope.\newlineWe know the slope mm is 55, and we have the points (−7,−6)(-7, -6) and (−6,t)(-6, t). Let's denote (−7,−6)(-7, -6) as (x1,y1)(x_1, y_1) and (−6,t)(-6, t) as (x2,y2)(x_2, y_2).\newlineUsing the slope formula:\newline5=t−(−6)−6−(−7)5 = \frac{t - (-6)}{-6 - (-7)}
  3. Simplify equation and solve: Simplify the equation and solve for tt.5=t+6−6+75 = \frac{t + 6}{-6 + 7}5=t+615 = \frac{t + 6}{1}Now, multiply both sides by 11 to isolate (t+6)(t + 6) on one side:5×1=t+65 \times 1 = t + 6
  4. Subtract to solve for tt: Subtract 66 from both sides to solve for tt.5=t+65 = t + 65−6=t5 - 6 = tt=−1t = -1

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