Graphing an involves two main steps.
- Plotting the .
- Shading half of the to show the .
Boundary Line
To graph the inequality, we first have to draw the boundary line. The of a boundary line is written by replacing the inequality symbol in the inequality with an equals sign.
Inequality3y+x > 4 Boundary Line 3y+x = 4
To draw this line, we will first rewrite the equation in .
Now that the equation is in slope-intercept form, we can identify the
m and
(0,b).
y=-31x+34
We will plot the
y-intercept
(0,34), then use the slope
m=-31 to plot another point on the line. Connecting these points with a dashed line will give us the boundary line of our inequality. Note that the boundary line is dashed,
not solid, because the inequality is .
Shading the Plane
To decide which side of the boundary line to shade, we will substitute a test point that is not on the boundary line into the given inequality. If the substitution creates a true statement, we shade the that includes the test point. Otherwise, we shade the opposite region. Let's use
(0,0) as our test point.
3y+x>4
3(0)+0>?4
0+0>?4
0≯4 ×
Since the substitution of the test point did not create a true statement, we will shade the region that does not contain the point.