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## which of the following graphs shows the graph of this equation?

Without seeing any of your graph choices, no way to directly answer 🙂 But we do know some things: because there are no exponents (x2 or x3, etc.), we already know that this is a “linear equation”. Linear means straight line, and the graph is a straight line. Solve for y:

y+1 = 2(x-1) => y=2x-2+1 => y=2x-1. Insert some numbers for x and solve for y:

x = 0: y = 2(0)-1 = -1

x = +1: y = 2(1)-1 = +1

x = +2: y = 2(2)-1 = +3

x = -1: y = 2(-1)-1 = -3

x = -2: y = 2(-2)-1 = -5

If we plot those x and y values on a graph, we see a straight line going from upper right to lower left, crossing the x-axis just to the right of (0,0), where the X and Y axes intersect (meet).

Since slope is defined by the change in y divided by the change in x, take any two y-values and their cooresponding (matching) x-values to get the slope of our straight line: for example, at x = 0, y = -1, and at x = +2, y = +3

As x goes from 0 to +2, y goes from -1 to +3, so the slope is y1 – y2 / x1 – x2 ,

or (-1) – (+3) / (0) – (+2) = -4/-2 = +2. The slope is +2.

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