Question

Which shows the graph of the solution set of 6x + 4y < 12?

Answer 1

graph B is the correct solution

Answer 2

The graph on the left shows the solution set of
`$6 x+4 y < 12$`.

First, we can rewrite the inequality as
`$y < -(3)/(2) x+3$`. This puts the equation in slop intercept form, where the y-intercept is 3 and the slope is
`$-(3)/(2)$`.

The slope is negative, so the line slants downward as we move from left to right.

The y-intercept is 3 , so the line crosses the y-axis at (0,3).

Since the inequality is less than, the shaded area is below the line. This means that any point below the line is a solution to the inequality.

The graph on the right shows the solution set of
`$6 x+4 y > 12$`. The slope and y-intercept are the same, but the inequality is reversed, so the shaded area is above the line.

Therefore, the graph on the left is the correct one for
`$6 x+4 y < 12$`.