Answer
Only (a), (c), and (g)'s equations might have the graph shown.
Work Step by Step
We can see that the graph has a positive x-intercept and a positive y-intercept, so we should find the intercepts of the given equations to find out if their x and y-intercepts are positive.
(a) x-intercept:
$2x+3(0)=6$
$2x=6$
$x=3 \checkmark$
y-intercept:
$2(0)+3y=6$
$3y=6$
$y=2\checkmark$
(b) x-intercept:
$2x-3(0)=6$
$2x=6$
$x=3 \checkmark$
y-intercept:
$2(0)-3y=6$
$-3y=6$
$y=-2$ nope
(c) x-intercept:
$3x+4(0)=12$
$3x=12$
$x=4 \checkmark$
y-intercept:
$3(0)+4y=12$
$4y=12$
$y=3\checkmark$
(d) x-intercept:
$x-0=1$
$x=1\checkmark$
y-intercept:
$0-y=1$
$y=-1$ nope
(e) x-intercept:
$x-0=-1$
$x=-1$ nope
(f) x-intercept:
$0=-2x-1$
$2x=-1$
$x=-1/2$ nope
(g) x-intercept:
$0=-\frac{1}{2}x+10$
$\frac{1}{2}x=10$
$x=20 \checkmark$
y-intercept:
$y=-\frac{1}{2}(0)+10$
$y=10 \checkmark$
(h) x-intercept:
$0=x+4$
$x=-4$ nope
Only (a), (c), and (g)'s equations might have the graph shown.