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Answer:
y ≥ -2/3x +2
Step-by-step explanation:
The y-intercept of the boundary line is y=2.
The next grid intersection to the right appears to be the x-intercept at x=3, which represents a "rise" of -2 and a "run" of +3 from the y-intercept.
At this point, we know the slope (rise/run = -2/3) and the y-intercept (+2) of the boundary line. We see it is a solid line, and shading is above it. This means the inequality could be ...
y = mx + b . . . . . . . . . equation for a line with slope m and y-intercept b
y ≥ -2/3x +2 . . . . . equation for the graphed inequality
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<em>Alternate solution</em>
We observe that the y-intercept is +2, and the x-intercept is +3. The equation of the boundary line can be written in intercept form as ...
x/x-intercept = y/y-intercept = 1
As noted above, the line is shaded where both x- and y-values are greater than or equal to those on the line. So, the "intercept form" of the inequality could be ...
x/3 +y/2 ≥ 1
Often, we don't like fractions, so we can multiply by 6 to put this in standard form:
2x +3y ≥ 6
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<em>Additional comment</em>
Any of these highlighted inequalities is "an inequality" that describes the graph. We don't know if you're required to write the inequality in a specific form.
