(y − 4) > −(2x + 1) (how do you graph it?)

Answer 1

The goal here is to get the inequality in the form of y = mx+b. It's much easier to graph this way. So, you just solve for y.

(y-4) > -(2x+1) Distribute the negative

(y-4) > -2x -1 Add 4 to both sides

y > -2x -1 +4 or

y > -2x +3

Now we can graph it by using the y-intercept. This is where the graph crosses the Y Axis and the corresponding X value is 0.

y > -2(0) + 3 So, y > 3

Mark the point (0,3) on the graph. Since slope = rise / run, we know that the slope is -2 / 1. So, count down 2 units and over 1 unit. Now you have 2 points and can graph the line. It will be a dotted line because the inequality shows > and not ≥. If it was ≥, then it would be solid line. Once you graph the inequality, you have to chose a test point to know whether to shade underneath or above the line. The easiest test point is the origin (0,0). Plug in the values and if its true, shade on the side of your test point. If it is false, shade on the side of the line that does not contain the test point.

0 > -2(0) + 3 This is false, so shade on the side that doesn't contain the origin.