Let's go through each answer choice by itself. What we're looking for in each is the slope and y intercept to see whether it could be a possibility on the graph.
A ) It has a slope of 3, meaning it is positive and has an upward slope, so far so good. It has a y intercept of -2, below the x axis. Both of these are true for the graph, so this COULD be a possibility.
B ) Converting the standard form equation into slope intercept form -4x+2y=-6 +4x +4x 2y=4x-6 /2 /2 y=2x-3 We see the slope is positive meaning it has an upward slope, which matches the graph, and has a negative y intercept, which also matches the graph, meaning it COULD be a possibility.
C ) This is NOT a possibility, because, if y=-10 were graphed, it would be a line with zero slope, which does not match the graph, meaning it COULD NOT be a possibility
D ) First, we must convert the standard form equation into slope intercept form. 2x-3y=-9 -2x -2x -3y=-2x-9 /-3 /-3 y=2/3x+3 The slope is positive, meaning it has a upward slope, which matches the graph, however the y intercept is positive, and over the x axis, meaning it COULD NOT be a possibility.