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A line has a slope of −3-3 and includes the points (10,a)(10,a) and (9,1)(9,1). What is the value of aa?\newlinea = ____

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Full solution

Q. A line has a slope of −3-3 and includes the points (10,a)(10,a) and (9,1)(9,1). What is the value of aa?\newlinea = ____
  1. Use Slope Formula: To find the value of aa, we can use the slope formula, which is y2−y1x2−x1=slope\frac{y_2 - y_1}{x_2 - x_1} = \text{slope}. Here, we have two points (x1,y1)=(9,1)(x_1, y_1) = (9, 1) and (x2,y2)=(10,a)(x_2, y_2) = (10, a), and the slope is given as −3-3.
  2. Substitute Values: Substitute the given values into the slope formula: (a−1)/(10−9)=−3(a - 1) / (10 - 9) = -3.
  3. Simplify Equation: Simplify the denominator 10−910 - 9 to get 11, so the equation becomes (a−1)/1=−3(a - 1) / 1 = -3.
  4. Isolate Term: Multiply both sides by 11 to isolate the term (a−1)(a - 1) on one side: a−1=−3×1a - 1 = -3 \times 1.
  5. Solve for aa: Simplify the right side of the equation: a−1=−3a - 1 = -3.
  6. Calculate Value: Add 11 to both sides of the equation to solve for aa: a=−3+1a = -3 + 1.
  7. Calculate Value: Add 11 to both sides of the equation to solve for aa: a=−3+1a = -3 + 1.Calculate the value of aa: a=−2a = -2.

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