Graphing Linear Equations In Two Variables Worksheets
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6GRAPHING LINEAR EQUATIONS IN TWO VARIABLES
To graph a linear inequality with one variable we use the number line. To graph a linear inequality
with two variables we use a two-dimensional graph. As with linear equations, linear inequalities can be
written in standard form or slope intercept form.
+
<
+
>
Ax By C
or
Ax By C
Standard Form:
+
≤
+
≥
Ax By C
or
Ax By C
<
+
>
+
y mx b
or
y mx b
Slope-Intercept Form:
≤
+
≥
+
y mx b
or
y mx b
To graph a linear inequality with two variables it is probably easier and recommended to change it to
slope intercept form. There are two important rules to remember when graphing a linear inequality. If
the inequality sign is > or <, the line is dashed. If the inequality is ≥ or ≤ , then the line is solid. Also,
for inequalities that are greater than > or greater or equal to ≥ the graph needs to be shaded above the
line. For inequalities that are less than < or less or equal to ≤ the graph needs to be shaded below the
line.
+
≥ :
Examples:
Graph the solutions of 3
x
2
y
6
Step 1 – Since the equation is in standard form, change it to slope intercept form.
+
≥
→
≥ −
+
3
x
2
y
6
2
y
3
x
6
−
+
3
x
6
≥
y
2
3
≥ −
+
← Slope-Intercept Form
y
x
3
2
Step 2 – Graph the slope-intercept form equation. Since the inequality has the
sign ≥ the line is solid.
Step 3 – Since the equation has the sign ≥ , the graph is shaded above the line.
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