Question

Which of the following equations might have the graph shown? (More than one answer is possible.)

$$\begin{gathered} \left(a\right)2x+3y=6 \\ \left(b\right)2x-3y=6 \\ \left(c\right)3x+4y=12 \\ \left(d\right)x-y=1 \\ \left(e\right)x-y=-1 \\ \left(f\right)y=-2x-1 \\ \left(g\right)y=-\frac{1}{2}x+10 \\ \left(h\right)y=x+4 \end{gathered}$$

Short answer

The following equations describes the given line

$$\begin{gathered} \left(a\right)2x+3y=6 \\ \left(c\right)3x+4y=12 \\ \left(g\right)y=-\frac{1}{2}x+10 \end{gathered}$$

Step-by-step solution

Given information

We are given graph and several equations.

Step 2: Explanation for correct options

The lines shown in the graph has positive y-intercept and also the slope of the line is negative

Consider the equation

$$\begin{gathered} \left(a\right)2x+3y=6 \\ y=-\frac{2}{3}+6 \\ \left(c\right)3x+4y=12 \\ y=-\frac{3}{4}x+3 \\ \left(g\right)y=-\frac{1}{2}x+10 \end{gathered}$$

In all the above options the slope is negative and y-intercept is positive

Hence the graph can describe the given lines

Explanation for other options

Consider the equations

$$\begin{gathered} \left(b\right)2x-3y=6 \\ y=\frac{2}{3}x+2 \\ \left(d\right)x-y=1 \\ y=x-1 \\ \left(e\right)x-y=-1 \\ y=x+1 \\ \left(f\right)y=-2x-1 \\ \left(h\right)y=x+4 \end{gathered}$$

From the above options options b) ,d) ,e),h) have positive slope

And option f) has negative y-intercept

Hence the graph can not be described by these lines

Conclusion

The graph can describe the given lines

$$\begin{gathered} \left(a\right)2x+3y=6 \\ \left(c\right)3x+4y=12 \\ \left(g\right)y=-\frac{1}{2}x+10 \end{gathered}$$