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A line has a slope of −2-2 and includes the points (6,−1)(6,-1) and (8,k)(8,k). What is the value of kk?\newlinek=k = ____

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Full solution

Q. A line has a slope of −2-2 and includes the points (6,−1)(6,-1) and (8,k)(8,k). What is the value of kk?\newlinek=k = ____
  1. Identify formula for slope: Identify the formula for the slope between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2): slope=y2−y1x2−x1\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}. Here, we know the slope −2-2, one point (6,−1)(6, -1), and part of another point (8,k)(8, k).
  2. Plug in known values: Plug in the known values into the slope formula: −2=(k−(−1))/(8−6)-2 = (k - (-1)) / (8 - 6). Simplify the equation: −2=(k+1)/2-2 = (k + 1) / 2.
  3. Solve for kk: Solve for kk: Multiply both sides by 22 to get rid of the denominator: −4=k+1-4 = k + 1.
  4. Subtract to isolate kk: Subtract 11 from both sides to isolate kk: −4−1=k-4 - 1 = k. So, k=−5k = -5.

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