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The points (7,k)(7,k) and (9,3)(9,3) fall on a line with a slope of 44. What is the value of kk?\newlinek=___k = \_\_\_

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Full solution

Q. The points (7,k)(7,k) and (9,3)(9,3) fall on a line with a slope of 44. What is the value of kk?\newlinek=___k = \_\_\_
  1. Set up slope equation: Use the slope formula to set up the equation. Slope = y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}. Here, slope = 44, (x1,y1)=(7,k)(x_1, y_1) = (7, k), and (x2,y2)=(9,3)(x_2, y_2) = (9, 3).\newline4=3−k9−74 = \frac{3 - k}{9 - 7}
  2. Simplify and solve for kk: Simplify the denominator and solve for kk.4=3−k24 = \frac{3 - k}{2}Multiply both sides by 22 to eliminate the fraction.4×2=(3−k)×224 \times 2 = \frac{(3 - k) \times 2}{2}8=3−k8 = 3 - k
  3. Rearrange to find kk: Rearrange the equation to solve for kk.8=3−k8 = 3 - k8−3=−k8 - 3 = -k5=−k5 = -kk=−5k = -5

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