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A line has a slope of 33 and includes the points (1,a)(1,a) and (3,10)(3,10). What is the value of aa?\newlinea = ____

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Full solution

Q. A line has a slope of 33 and includes the points (1,a)(1,a) and (3,10)(3,10). What is the value of aa?\newlinea = ____
  1. Understand the slope formula: Understand the slope formula.\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 for slope (mm) is:\newlinem=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}\newlineGiven that the slope (mm) is 33, we can use the points (1,a)(1, a) and (3,10)(3, 10) to set up the equation.
  2. Plug values into formula: Plug the given values into the slope formula.\newlineUsing the points (1,a)(1, a) and (3,10)(3, 10), we have:\newline3=10−a3−13 = \frac{10 - a}{3 - 1}
  3. Solve for a: Solve for a.\newlineFirst, simplify the denominator:\newline3=10−a23 = \frac{10 - a}{2}\newlineNow, multiply both sides by 22 to isolate the term with a:\newline3×2=(10−a)3 \times 2 = (10 - a)\newline6=10−a6 = 10 - a\newlineNext, add aa to both sides to get aa by itself:\newline6+a=106 + a = 10\newlineFinally, subtract 66 from both sides to find the value of aa:\newlinea=10−6a = 10 - 6\newlinea=4a = 4

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