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A line with a slope of 22 passes through the points (6,9)(6,9) and (4,u)(4,u). What is the value of uu?

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Full solution

Q. A line with a slope of 22 passes through the points (6,9)(6,9) and (4,u)(4,u). What is the value of uu?
  1. Identify Points: To find the value of uu, we can use the slope formula, which is (y2−y1)/(x2−x1)=slope(y_2 - y_1) / (x_2 - x_1) = \text{slope}. We know the slope is 22, and we have the points (6,9)(6,9) and (4,u)(4,u). Let's denote (6,9)(6,9) as (x1,y1)(x_1,y_1) and (4,u)(4,u) as (x2,y2)(x_2,y_2).
  2. Apply Slope Formula: Now we can plug the known values into the slope formula: (u−9)/(4−6)=2(u - 9) / (4 - 6) = 2. We need to solve for uu.
  3. Simplify Equation: Simplify the denominator: (u−9)/(−2)=2(u - 9) / (-2) = 2. To solve for uu, we can multiply both sides by −2-2 to get rid of the denominator.
  4. Multiply by −2-2: After multiplying both sides by −2-2, we get u−9=−4u - 9 = -4. Now, we can add 99 to both sides to solve for uu.
  5. Add 99: Adding 99 to both sides gives us u=−4+9u = -4 + 9.
  6. Calculate Value: Finally, we calculate u=5u = 5. So the value of uu is 55.

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