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A line with a slope of −6-6 passes through the points (−1,u)(-1,u) and (−3,2)(-3,2). What is the value of uu?\newlineu = ____

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Full solution

Q. A line with a slope of −6-6 passes through the points (−1,u)(-1,u) and (−3,2)(-3,2). 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 the coordinates of two points on the line. We know the slope is −6-6, and we have the points (−1,u)(-1, u) and (−3,2)(-3, 2).
  2. Plug in Values: Let's plug the known values into the slope formula: (−6)=(2−u)/(−3−(−1))(-6) = (2 - u) / (-3 - (-1)).
  3. Simplify Denominator: Simplify the denominator of the fraction: (−6)=2−u−3+1(-6) = \frac{2 - u}{-3 + 1}.
  4. Calculate Denominator: Calculate the denominator: (−6)=(2−u)(−2)(-6) = \frac{(2 - u)}{(-2)}.
  5. Isolate Variable: To find the value of uu, we need to solve for uu in the equation: (−6)=(2−u)/(−2)(-6) = (2 - u) / (-2). Multiply both sides by −2-2 to get rid of the fraction: (−6)×(−2)=2−u(-6) \times (-2) = 2 - u.
  6. Perform Subtraction: Perform the multiplication: 12=2−u12 = 2 - u.
  7. Simplify Equation: Now, we need to isolate uu. Subtract 22 from both sides of the equation: 12−2=2−u−212 - 2 = 2 - u - 2.
  8. Multiply by −1-1: Simplify the equation: 10=−u10 = -u.
  9. Calculate Final Value: To solve for uu, multiply both sides by −1-1: 10×(−1)=−u×(−1)10 \times (-1) = -u \times (-1).
  10. Calculate Final Value: To solve for uu, multiply both sides by −1-1: 10×(−1)=−u×(−1)10 \times (-1) = -u \times (-1).Calculate the final value of uu: −10=u-10 = u.

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