Question

a system of equations is graphed here. which system of equations does the graph represent? A) y = 3x + 2y = -2x + 5 B) y = 3x - 2 y = 2x + 5 C) y = -3x + 2 y = 2x - 5 D) y = -3x - 2 y = -2x - 5

Answer 1

Notice that the line with negative slope has a y-intercept of 5 and the line with positive slope has a y-intercept of 2.

On the other hand, the slope of the line with negative slope is -2, while the slope of the line with positive slope is 3 (This can be identified since in one case, the value of y decreases by 2 for each increase of 1 unit in x, and in the other, the value of y increases by 3 for each increase of 1 unit in x).

Using the y-intercept form to represent each line, the system of equations represented by the graph must be equivalent to:

$\begin{gathered} y=-2x+5 \\ y=3x+2 \end{gathered}$

From the given options, the one that displays the correct system of equations is option A.

Therefore, the answer is:

$\begin{gathered} A) \\ y=3x+2 \\ y=-2x+5 \end{gathered}$