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The points (−8,6)(-8,6) and (−7,k)(-7,k) fall on a line with a slope of 22. What is the value of kk?\newlinek=___k = \_\_\_

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Full solution

Q. The points (−8,6)(-8,6) and (−7,k)(-7,k) fall on a line with a slope of 22. What is the value of kk?\newlinek=___k = \_\_\_
  1. Calculate Slope Formula: Calculate the slope using the formula for slope between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2): y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}. Here, x1=−8x_1 = -8, y1=6y_1 = 6, x2=−7x_2 = -7, and y2=ky_2 = k.\newlineSlope formula: k−6−7+8\frac{k - 6}{-7 + 8}
  2. Simplify and Set Equal: Simplify the denominator and set the slope equal to 22. k−61=2\frac{k - 6}{1} = 2
  3. Solve for k: Solve for k by isolating k on one side of the equation. \newlinek−6=2k - 6 = 2\newlinek=2+6k = 2 + 6
  4. Find kk Value: Add the numbers to find kk.k=8k = 8

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