To solve this question, we need to find the x-intercepts and the y-intercepts for each of the equations. After having these values, we will have a pair of points for one equation, and another pair of points for the other equation.
We can proceed as follows:
First case:
We can find the y-intercept if we have x = 0. Then, the y-intercept is:
[tex]y=-\frac{1}{4}x+3,x=0\Rightarrow y=3[/tex]
Similarly, the x-intercept is (for y = 0, we then have x):
[tex]0=-\frac{1}{4}x+3\Rightarrow-3=-\frac{1}{4}x\Rightarrow-4\cdot(-3)=-4\cdot(-\frac{1}{4}x)\Rightarrow12=x\Rightarrow x=12[/tex]
Then, for the first equation, we have that the y-intercept is (0, 3), and the x-intercept is (12,0). These two points are important to graph this equation.
Second Case:
We can proceed in the same way to find the y-intercept and the x-intercept.
[tex]y=\frac{3}{4}x-1,x=0\Rightarrow y=-1[/tex]
Then, the y-intercept is (0, -1).
The x-intercept is
[tex]0=\frac{3}{4}x-1\Rightarrow\frac{3}{4}x=1\Rightarrow\frac{4}{3}\cdot\frac{3}{4}x=\frac{4}{3}\cdot1\Rightarrow x=\frac{4}{3}[/tex]
Hence, the x-intercept is (4/3, 0).
Having all of this information, we can graph the first line using the points:
The y-intercept is (0, 3)
The x-intercept is (12,0)
And then, we can graph the second line using the points:
The y-intercept is (0, -1)
The x-intercept is (4/3, 0).
The graph is
And the solution is the point where both lines intercept each other, that is the point x = 4, and y = 2.
If we see the answer choices we have that the answer is the second graph.
