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A line with a slope of 99 passes through the points (2,v)(2,v) and (3,1)(3,1). What is the value of vv?

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Full solution

Q. A line with a slope of 99 passes through the points (2,v)(2,v) and (3,1)(3,1). What is the value of vv?
  1. Understand slope concept: Understand the concept of slope. The slope of a line is the ratio of the change in the yy-coordinate to the change in the xx-coordinate between two points on the line. The formula for slope (mm) when given two points ((x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2)) is: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}
  2. Apply slope formula: Apply the slope formula to the given points and slope.\newlineWe know the slope mm is 99, and we have the points (2,v)(2, v) and (3,1)(3, 1). Let's plug these values into the slope formula:\newline9=1−v3−29 = \frac{1 - v}{3 - 2}
  3. Solve for v: Solve for v.\newlineNow we need to solve the equation for v:\newline9=1−v9 = 1 - v\newlineTo isolate vv, we'll add vv to both sides and subtract 99 from both sides:\newline9+v=19 + v = 1\newlinev=1−9v = 1 - 9\newlinev=−8v = -8

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