# How do you graph the inequality 3/4x + 1/4y > 1?

May 26, 2016

Draw the straight line $\frac{3 x + y}{4} = 1$ that passes through$\left(\frac{4}{3} , 0\right) \mathmr{and} \left(0 , 4\right)$. Shade the region above this line in the positive y-direction. Enter therein the given inequality.

#### Explanation:

The given inequality can be rearranged to the form $y > 4 - 3 x$

Draw the straight line $y = 4 - 3 x$ that passes through$\left(\frac{4}{3} , 0\right) \mathmr{and} \left(0 , 4\right)$.

Shade the region above this line in the positive y-direction.

Enter therein the given inequality.

For any point (x, y) in the shaded region, $y > 4 - 3 x$, and so, $\frac{y}{4} + \frac{3 x}{4} > 1$.