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A line with a slope of 77 passes through the points (−7,4)(-7,4) and (−8,u)(-8,u). What is the value of uu?\newlineu = ____

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Full solution

Q. A line with a slope of 77 passes through the points (−7,4)(-7,4) and (−8,u)(-8,u). What is the value of uu?\newlineu = ____
  1. Use Slope Formula: To find the value of uu, we can use the slope formula, which is y2−y1x2−x1=slope\frac{y_2 - y_1}{x_2 - x_1} = \text{slope}, where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are two points on the line. We know the slope is 77, and we have the points (−7,4)(-7, 4) and (−8,u)(-8, u). Let's plug these values into the slope formula.
  2. Plug in Values: The slope formula with our known values is (u−4)/(−8−(−7))=7(u - 4) / (-8 - (-7)) = 7. Simplify the denominator to get (u−4)/(−8+7)=7(u - 4) / (-8 + 7) = 7.
  3. Simplify Equation: Now we have (u−4)/(−1)=7(u - 4) / (-1) = 7. To find uu, we need to solve for it by multiplying both sides of the equation by −1-1 to get u−4=−7u - 4 = -7.
  4. Isolate Variable: Finally, we add 44 to both sides of the equation to isolate uu, which gives us u=−7+4u = -7 + 4.
  5. Calculate Final Value: Calculating the sum, we get u=−3u = -3. This is the value of uu for the point (−8,u)(-8, u) on the line with a slope of 77.

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