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A line with a slope of −4-4 passes through the points (−2,k)(-2,k) and (−1,−8)(-1,-8). What is the value of kk?\newlinek = ____

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Full solution

Q. A line with a slope of −4-4 passes through the points (−2,k)(-2,k) and (−1,−8)(-1,-8). What is the value of kk?\newlinek = ____
  1. Understand slope concept: Understand the concept of slope. The 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) when given two points ((x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2)) is: m=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 −4-4, and we have the points (−2,k)(-2, k) and (−1,−8)(-1, -8). Let's plug these into the slope formula:\newline−4=−8−k−1−(−2)-4 = \frac{-8 - k}{-1 - (-2)}
  3. Simplify denominator: Simplify the denominator of the slope equation.\newline−4=−8−k−1+2-4 = \frac{-8 - k}{-1 + 2}\newline−4=−8−k1-4 = \frac{-8 - k}{1}
  4. Solve for kk: Solve for kk.\newlineNow we multiply both sides by 11 to get rid of the denominator:\newline−4×1=−8−k-4 \times 1 = -8 - k\newline−4=−8−k-4 = -8 - k
  5. Isolate kk: Add 88 to both sides to isolate kk.\newline−4+8=−8+8−k-4 + 8 = -8 + 8 - k\newline4=−k4 = -k
  6. Multiply to solve kk: Multiply both sides by −1-1 to solve for kk.4×−1=−k×−14 \times -1 = -k \times -1−4=k-4 = k

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