Answer:
y < 2x +6
Explanation:
You want an inequality for the given graph.
What to do
Here are some steps you can follow, in no particular order.
- identify the type of boundary line: solid or dashed (dashed)
- locate the shading: above the line or below it (below)
- locate the y-intercept (+6)
- identify the slope (rise/run = 4/2 = 2)
When you have this information, you can write the inequality in slope-intercept form.
Using the information
When the boundary line is dashed, the inequality symbol you use will not include the "or equal to" case. It will be one of < or >.
When the shading is below the line, the values of y that satisfy the inequality will be less than (<) those on the boundary line. If shading is above, the y-values will be greater than (>) those on the line.
The slope and intercept go into the inequality like this:
y < mx + b . . . . . . where m is the slope, and b is the y-intercept
For a dashed line, shaded below, with m=2 and b=6, the inequality is ...
y < 2x +6
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Additional comment
There are two points identified on the boundary line: (-2, 2) and (0, 6). The slope formula can be used to find the slope:
m = (y2 -y1)/(x2 -x1)
m = (6 -2)/(0 -(-2)) = 4/2 = 2
The point (0, 6) on the y-axis is the y-intercept. The y-value there is 6.
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