Solve each of a linear inequalities graphically. 3x+y<6 x+y>4?

Answer 1

Here's how I would do these.

Rewrite the inequality so that y is on one side by itself. For the first inequality, this would be

y < 6 - 3x

First, get the "border" of the region. Write the inequality as an equality. For your first inequality, this would be

y = 6 - 3x

(or in slope-intercept form if you prefer, y = -3x + 6)

To draw this line, I think it's easiest to simply find two points on the line (by choosing convenient values for x and putting each into the equation to get the corresponding y-value). For example, (0,6) (the y-intercept) and (2,0) are on the line. So on a set of coordinate axes, plot these two points and lightly draw the line that passes through them. This is the "border" Since it is a strict inequality, it should be graphed as a dotted line. The region satisfying the inequality is the part below the dotted line because the inequality is "y < " (you can confirm that you have chosen correct region by picking any (x,y) point in the region and checking that it satisfies the inequality).

Shade this region.

The second inequality can be handled in exactly the same way.