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A line that includes the points (−1,2)(-1,2) and (−3,a)(-3,a) has a slope of −2-2. What is the value of aa?\newlinea = ____

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Full solution

Q. A line that includes the points (−1,2)(-1,2) and (−3,a)(-3,a) has a slope of −2-2. What is the value of aa?\newlinea = ____
  1. Understand the formula: Understand the formula for the slope of a line.\newlineThe slope mm of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}.
  2. Apply the slope formula: Apply the slope formula to the given points and slope.\newlineWe know the slope mm is −2-2, and we have the points (−1,2)(-1, 2) and (−3,a)(-3, a). Let's denote (−1,2)(-1, 2) as (x1,y1)(x_1, y_1) and (−3,a)(-3, a) as (x2,y2)(x_2, y_2). According to the slope formula:\newline−2=a−2−3−(−1)-2 = \frac{a - 2}{-3 - (-1)}
  3. Simplify and solve: Simplify the denominator and solve for aa.−2=a−2−3+1-2 = \frac{a - 2}{-3 + 1}−2=a−2−2-2 = \frac{a - 2}{-2}Now, multiply both sides by −2-2 to isolate (a−2)(a - 2).−2×−2=(a−2)×−2−2-2 \times -2 = (a - 2) \times \frac{-2}{-2}4=a−24 = a - 2
  4. Find the value of aa: Add 22 to both sides to find the value of aa.4+2=a−2+24 + 2 = a - 2 + 26=a6 = a

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