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A line has a slope of 99 and includes the points (−2,v)(-2,v) and (−4,−9)(-4,-9). What is the value of vv?\newlinev = ____

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Full solution

Q. A line has a slope of 99 and includes the points (−2,v)(-2,v) and (−4,−9)(-4,-9). What is the value of vv?\newlinev = ____
  1. Identify Slope Formula: To find the value of vv, we can use the slope formula, which is (change in y)/(change in x)=slope(\text{change in } y) / (\text{change in } x) = \text{slope}. We know the slope mm is 99, and we have two points: (−2,v)(-2, v) and (−4,−9)(-4, -9). Let's denote the first point as (x1,y1)(x_1, y_1) and the second point as (x2,y2)(x_2, y_2).
  2. Plug in Known Values: First, let's plug the known values into the slope formula: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}. We get 9=(−9−v)(−4−(−2))9 = \frac{(-9 - v)}{(-4 - (-2))}.
  3. Simplify Denominator: Simplify the denominator of the fraction: −4−(−2)=−4+2=−2-4 - (-2) = -4 + 2 = -2. Now we have 9=(−9−v)/(−2)9 = (-9 - v) / (-2).
  4. Eliminate Fraction: To solve for vv, we need to get rid of the fraction by multiplying both sides of the equation by −2-2. This gives us −18=−9−v-18 = -9 - v.
  5. Isolate Variable vv: Now, we add 99 to both sides of the equation to isolate vv on one side: −18+9=−9−v+9-18 + 9 = -9 - v + 9. This simplifies to −9=−v-9 = -v.
  6. Solve for v: Finally, we multiply both sides by −1-1 to solve for vv: −1×−9=−1×−v-1 \times -9 = -1 \times -v. This gives us v=9v = 9.

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