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

The correct answer is D. Choice D is correct. In the xy -plane, the graph of the equation y = m x + b , where m and b are constants, is a line with slope m and y -intercept (0, b) . Therefore, the graph of y = 2 x - 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.

Note: The slope is 2 and the y-intercept is -5, so the line rises 2 units for every 1 unit right and crosses the y-axis at -5.

SAT Question a8e6bd75: Answer, Explanation & Desmos Solution

Choice A

Choice A is incorrect. The graph of $y = 2 x - 5$ in the $x y$ -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 $\frac{1}{2}$ , not $2$ .

Choice B

Choice B is incorrect. The graph of $y = 2 x - 5$ in the $x y$ -plane is a line with slope $2$ and a $y$ -intercept at $(0, - 5)$ . The graph in choice B crosses the $y$ -axis at $(0, - 5)$ ; however, the slope of this line is $- 2$ , not $2$ .

Choice C

Choice C is incorrect. The graph of $y = 2 x - 5$ in the $x y$ -plane is a line with slope $2$ and a $y$ -intercept at $(0, - 5)$ . The graph in choice C has a slope of $2$ ; however, the graph crosses the $y$ -axis at $(0, 5)$ , not $(0, - 5)$ .

Explanation

Enter in Desmos:

Why the other choices are wrong

SAT Question a8e6bd75: Linear Functions answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong