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Which of the following is the graph of the equation y = 2x − 5 in the xy-plane?

Answer»




Solution :In the xy-plane, the graph of the equation y = mx + b, where m and b are constants, is a LINE with slope m and y-intercept (0, b). Therefore, the graph of y = 2x − 5 in the xy-plane is a line with slope 2 and a y-intercept (0, −5). Having a slope of 2 means that for each INCREASE in x by 1, the value of y INCREASES by 2. Only the graph in choice D has a slope of 2 and crosses the y-axis at (0, −5). Therefore, the graph shown in choice D must be the correct answer.
Choices A, B, and C are incorrect. The graph of y = 2x − 5 in the xy-plane is a line with slope 2 and a y-intercept at (0, −5). The graph in choice A crosses the y-axis at the point (0, 2.5), not (0, −5), and it has a slope of `1/2`, not 2. The graph in choice B crosses the y-axis at (0, −5), however, the slope of this line is −2, not 2. The graph in choice C has a slope of 2, however, the graph crosses the y-axis at (0, 5), not (0, −5).


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