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Write the inequality that has been graphed in the given figure.
Write the inequality that has been
graphed in the given figure.
Here we can see that we have a
linear inequality. It’s a line. Now I also notice that this is a
dash line. Since it’s a dash line, that means
this inequality will be a less than or greater than. If it were a solid line, it would
have been a less than or equal to, or a greater than or equal to sign can be
used. So that means we now we’re gonna be
using a less than or a greater than sign.
Now notice looking at our line left
to right it’s increasing, and all of the shaded region is underneath that line. So if it were underneath the line,
that means it would be everything less than that line, so we know that our
inequality will be 𝑦 is less than. And we have to figure out the rest,
so we have to figure out what is this line.
So we need to find the slope and we
need to find 𝑏, the 𝑦 intercept. So our slope can be found by
looking at two points on our line and using it to see the rise over the run. So we went up four spaces and then
we had to run one space to the right, so our slope is four over one.
Now our 𝑦 intercept, 𝑏, is where
we cross the 𝑦-axis, and we cross that at negative three. Therefore, 𝑏 is negative
three. Therefore, the inequality that has
been graphed in this given figure is 𝑦 is less than four 𝑥 minus three.
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