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A line with a slope of 22 passes through the points (0,g)(0,g) and (−6,−6)(-6,-6). What is the value of gg?

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Full solution

Q. A line with a slope of 22 passes through the points (0,g)(0,g) and (−6,−6)(-6,-6). What is the value of gg?
  1. Slope Formula Calculation: We know the slope formula is (y2−y1)/(x2−x1)(y_2 - y_1) / (x_2 - x_1). We can use the points (0,g)(0,g) as (x1,y1)(x_1,y_1) and (−6,−6)(-6,-6) as (x2,y2)(x_2,y_2) to find the value of gg.\newlineSlope = (y2−y1)/(x2−x1)(y_2 - y_1) / (x_2 - x_1)\newline2=(−6−g)/(−6−0)2 = (-6 - g) / (-6 - 0)
  2. Solving for g: Now we solve for gg by multiplying both sides of the equation by −6-6 to get rid of the denominator.2×−6=(−6−g)2 \times -6 = (-6 - g)−12=−6−g-12 = -6 - g
  3. Isolating g: Next, we add 66 to both sides of the equation to isolate gg on one side.\newline−12+6=−6−g+6-12 + 6 = -6 - g + 6\newline−6=−g-6 = -g
  4. Final Solution for gg: Finally, we multiply both sides by −1-1 to solve for gg.\newline−1×−6=g-1 \times -6 = g\newline6=g6 = g

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