Which description of the graph of the linear equality y ≥ 7x – 4 is correct?

Answer 1

Since you did not provide any of the description choices, think about how you would graph this inequality.

Note the related equation (y = 7x - 4) is in slope intercept form. So the graph of the equation becomes the boundary of the inequality. What does that line look like? Since slope is positive, it slopes upward from left to right. The y-intercept is (0, -4) and the line also passes through a point 7 units above and 1 unit right of the y-intercept which is (1, 3).

The inequality states that y ≥ 7x-4, so the line will be solid. (As opposed to a broken line if the inequality stated y>7x-4).

The final thing you need to do is determine which side of the plane contains the solutions to the inequality. If you want to be certain, pick any point on either side of the line. Plug those coordinates into the inequality to see if the statement is true. If it is, the area that contains the point is the area you shade. If false, shade the other side.

I usually use (0,0) if it is not a point ON the line. When you plug into the inequality, the result is 0 ≥ 7(0) - 4.

Simplified, it is 0 ≥ -4. Since this is a true statement, the area containing (0,0) -- to the left of the line -- is shaded.