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A line that includes the points (6,5)(6,5) and (8,u)(8,u) has a slope of −4-4. What is the value of uu?\newlineu = ____

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Full solution

Q. A line that includes the points (6,5)(6,5) and (8,u)(8,u) has a slope of −4-4. What is the value of uu?\newlineu = ____
  1. Understand the formula: Understand the formula for the slope of a line.\newlineThe slope of a line is calculated by the difference in the yy-coordinates divided by the difference in the xx-coordinates between two points on the line. The formula is:\newlineslope (mm) = (y2−y1)/(x2−x1)(y_2 - y_1) / (x_2 - x_1)
  2. Apply the formula: Apply the slope formula to the given points and slope.\newlineWe are given the slope mm as −4-4, and two points (6,5)(6,5) and (8,u)(8,u). Let's denote (6,5)(6,5) as (x1,y1)(x_1, y_1) and (8,u)(8,u) as (x2,y2)(x_2, y_2). According to the slope formula:\newline−4=u−58−6-4 = \frac{u - 5}{8 - 6}
  3. Solve for u: Solve for u.\newlineNow we need to solve the equation for u:\newline−4=u−52-4 = \frac{u - 5}{2}\newlineMultiply both sides by 22 to isolate (u−5)(u - 5):\newline−4×2=u−5-4 \times 2 = u - 5\newline−8=u−5-8 = u - 5\newlineNow, add 55 to both sides to solve for u:\newline−8+5=u-8 + 5 = u\newline−3=u-3 = u

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