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1.1 Linear Functions - Graphs in slope-intercept, point-slope, standard form
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Which of the following is the graph of the equation y, equals 2 x minus 5 in the xy-plane?

A.

 

The figure presents the graph of a line in the x y-plane with the origin labeled O. The numbers negative five through five are indied on each axis. The line begins in quadrant 3 and moves upward and to the right. It crosses the x-axis at negative 5 and the y-axis at 2 point 5, ending in quadrant 1

 

B.

 

The figure presents the graph of a line in the x y-plane with the origin labeled O. The numbers negative five through five are indied on each axis. The line begins in quadrant 2 and moves downward and to the right. It crosses the x-axis at negative 2 point 5 and the y-axis at negative 5, ending in quadrant 4

 

C.

 

The figure presents the graph of a line in the x y-plane with the origin labeled O. The numbers negative five through five are indied on each axis. The line begins in quadrant 3 and moves upward and to the right. It crosses the x-axis at negative 2 point 5 and the y-axis at 5, ending in quadrant 1

 

D.

 

The figure presents the graph of a line in the x y-plane with the origin labeled O. The numbers negative five through five are indied on each axis. The line begins in quadrant 3 and moves upward and to the right. It crosses the y-axis at negative 5 and the x-axis at 2 point 5, ending in quadrant 1

 

Which of the following is the graph of the equation in the xy -plane?

Medium-difficulty · SAT Math · Linear Functions — Graphs in slope-intercept, point-slope, standard form. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer 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.

 

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