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A line has a slope of −6-6 and includes the points (0,k)(0,k) and (−3,10)(-3,10). What is the value of kk?\newlinek = ____

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Full solution

Q. A line has a slope of −6-6 and includes the points (0,k)(0,k) and (−3,10)(-3,10). What is the value of kk?\newlinek = ____
  1. Understand slope formula: Understand the slope formula.\newlineThe slope of a line is calculated by the change in yy divided by the change in xx (rise over run). The formula for slope (mm) 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 formula to points: Apply the slope formula to the given points and slope.\newlineWe know the slope mm is −6-6, one point is (−3,10)(-3, 10), and the other point is (0,k)(0, k). Plugging these into the slope formula, we get:\newline−6=k−100−(−3)-6 = \frac{k - 10}{0 - (-3)}
  3. Solve for k: Solve for k.\newlineTo find kk, we need to solve the equation from Step 22:\newline−6=k−103-6 = \frac{k - 10}{3}\newlineMultiply both sides by 33 to isolate (k−10)(k - 10):\newline−6×3=k−10-6 \times 3 = k - 10\newline−18=k−10-18 = k - 10\newlineNow, add 1010 to both sides to solve for kk:\newline−18+10=k-18 + 10 = k\newline−8=k-8 = k

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