Question

Which shows the graph of the solution set of 6x + 4y < 12? On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (3, 1). Everything below and to the left of the line is shaded. On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (3, 1). Everything above and to the right of the line is shaded. On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, 0). Everything to the left of the line is shaded. On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, 0). Everything to the right of the line is shaded.

Answer 1

(c) On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, 0). Everything to the left of the line is shaded.

Explanation:

You want a description of the graph of 6x +4y < 12.

Intercepts

The x-intercept will be the solution to ...

6x = 12 ⇒ x = 2, point (2, 0)

The y-intercept will be the solution to ...

4y = 12 ⇒ y = 3, point (0, 3)

Shading

The form of the inequality ...

x < ( )

tells you the shading is left of the line, and the line is dashed. That is, solution set values of x are less than those on the line. The "or equal to" case is not included, so the line is not included in the solution set.