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A line with a slope of −6-6 passes through the points (10,g)(10,g) and (9,1)(9,1). What is the value of gg?\newlineg = ____

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Full solution

Q. A line with a slope of −6-6 passes through the points (10,g)(10,g) and (9,1)(9,1). What is the value of gg?\newlineg = ____
  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) is given by: m=(y2−y1)(x2−x1)m = \frac{(y_2 - y_1)}{(x_2 - x_1)} Here, we are given the slope (mm) as −6-6 and two points (10,g)(10, g) and (9,1)(9, 1).
  2. Substitute values into formula: Substitute the given values into the slope formula.\newlineUsing the points (10,g)(10, g) as (x1,y1)(x_1, y_1) and (9,1)(9, 1) as (x2,y2)(x_2, y_2), we have:\newline−6=(1−g)(9−10)-6 = \frac{(1 - g)}{(9 - 10)}
  3. Solve for g: Solve for g.\newlineNow, we simplify the right side of the equation:\newline−6=1−g−1-6 = \frac{1 - g}{-1}\newlineMultiplying both sides by −1-1 to isolate (1−g)(1 - g), we get:\newline6=g−16 = g - 1
  4. Add 11 to solve gg: Add 11 to both sides of the equation to solve for gg.6+1=g6 + 1 = gg=7g = 7

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