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Algebra / Linear functions Difficulty: Easy

Which of the following is the graph of the equation $y, equals 2 x minus 5$ in the xy-plane?

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Explanation

Choice D is correct. In the xy-plane, the graph of the equation $y equals, m x plus b$ , where m and b are constants, is a line with slope m and y-intercept $with coordinates 0 comma b$ . Therefore, the graph of $y equals, 2 x minus 5$ in the xy-plane is a line with slope 2 and a y-intercept $with coordinates 0 comma negative 5$ . 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 $the point with coordinates 0 comma negative 5$ . Therefore, the graph shown in choice D must be the correct answer.

Choices A, B, and C are incorrect. The graph of $y equals, 2 x minus 5$ in the xy-plane is a line with slope 2 and a y-intercept at $the point with coordinates 0 comma negative 5$ . The graph in choice A crosses the y-axis at the point $with coordinates 0 comma 2 point 5$ , not $the point with coordinates 0 comma negative 5$ , and it has a slope of $one-half$ , not 2. The graph in choice B crosses the y-axis at $the point with coordinates 0 comma negative 5$ ; however, the slope of this line is $negative 2$ , not 2. The graph in choice C has a slope of 2; however, the graph crosses the y-axis at $the point with coordinates 0 comma 5$ , not $the point with coordinates 0 comma negative 5$ .