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A line that includes the points (5,a)(5,a) and (3,10)(3,10) has a slope of −6-6. What is the value of aa?\newlinea = ____

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Full solution

Q. A line that includes the points (5,a)(5,a) and (3,10)(3,10) has a slope of −6-6. What is the value of aa?\newlinea = ____
  1. Identify Points and Slope: Identify the given points and the slope. We have the points (5,a)(5, a) and (3,10)(3, 10) and the slope of the line is −6-6.
  2. Use Slope Formula: Use the slope formula to set up an equation.\newlineThe slope formula is (y2−y1)/(x2−x1)(y_2 - y_1) / (x_2 - x_1). Let's plug in our values.\newline−6=(10−a)/(3−5)-6 = (10 - a) / (3 - 5)
  3. Simplify Denominator: Simplify the denominator of the fraction. \newline−6=10−a−2-6 = \frac{10 - a}{-2}
  4. Multiply by −2-2: Multiply both sides of the equation by −2-2 to solve for aa.−6×(−2)=(10−a)-6 \times (-2) = (10 - a)12=10−a12 = 10 - a
  5. Isolate Variable aa: Isolate the variable aa by adding aa to both sides and subtracting 1212 from both sides.\newline12+a=1012 + a = 10\newlinea=10−12a = 10 - 12\newlinea=−2a = -2

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