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The points (2,9)(2,9) and (0,v)(0,v) fall on a line with a slope of 99. What is the value of vv?\newlinev = ____

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Full solution

Q. The points (2,9)(2,9) and (0,v)(0,v) fall on a line with a slope of 99. What is the value of vv?\newlinev = ____
  1. Given Points and Slope: We are given two points on a line: (2,9)(2,9) and (0,v)(0,v). We are also given the slope of the line, which is 99. The slope formula is (y2−y1)/(x2−x1)(y_2 - y_1) / (x_2 - x_1), where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are the coordinates of two points on the line. We can use this formula to find the value of vv.
  2. Plug in Values: Let's plug in the values into the slope formula. We have (x1,y1)=(2,9)(x_1, y_1) = (2, 9) and (x2,y2)=(0,v)(x_2, y_2) = (0, v). The slope mm is 99. So, according to the formula, we have:\newlinem=v−90−2m = \frac{v - 9}{0 - 2}
  3. Solve for vv: Now, we can solve for vv. Since the slope mm is 99, we have:\newline9=v−90−29 = \frac{v - 9}{0 - 2}\newlineThis simplifies to:\newline9=v−9−29 = \frac{v - 9}{-2}
  4. Multiply by −2-2: To find vv, we multiply both sides of the equation by −2-2:\newline9×−2=(v−9)9 \times -2 = (v - 9)\newlineThis gives us:\newline−18=v−9-18 = v - 9
  5. Add 99: Finally, we add 99 to both sides of the equation to solve for vv:\newline−18+9=v-18 + 9 = v\newlinev=−9v = -9

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