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When the equation y=2x−by = 2x - b, where bb is a constant, is graphed in the xyxy-plane, the line passes through the point (3,−1)(3, -1). What is the value of bb?

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Q. When the equation y=2x−by = 2x - b, where bb is a constant, is graphed in the xyxy-plane, the line passes through the point (3,−1)(3, -1). What is the value of bb?
  1. Identify Given Information: Identify the given information.\newlineWe have the equation of a line in the form y=mx−by = mx - b, where mm is the slope and bb is the y-intercept. The line passes through the point (3,−1)(3, -1).
  2. Substitute Point into Equation: Substitute the given point into the equation to solve for bb. The point (3,−1)(3, -1) gives us the values x=3x = 3 and y=−1y = -1. We can substitute these values into the equation y=2x−by = 2x - b to find bb. −1=2(3)−b-1 = 2(3) - b
  3. Solve for b: Perform the multiplication and solve for b.\newline−1=6−b-1 = 6 - b\newlineNow, we need to isolate bb by moving 66 to the other side of the equation.\newline−1−6=−b-1 - 6 = -b\newline−7=−b-7 = -b\newlineTo solve for bb, we multiply both sides by −1-1.\newlineb=7b = 7

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