How to graph an inequality?
Hi Selma. I'll presume that you mean linear variables.
It's actually quite easy. Let's take the example of
$\displaystyle 3y - 4x < 0$
This can be manipulated to give
$\displaystyle
y<\frac{4}{3}x
$
Now we just ignore the inequalities sign for the moment, and draw the graph of $\displaystyle y=\frac{4}{3}x$
Then, simply shade whichever side of the line does not match your inequality. In this scenario, we want the side where y is less than $\displaystyle \frac{4}{3}x$, so the section above the line is shaded as it does not fit the equality.
Note that as the line of $\displaystyle y=\frac{4}{3}x$ is not included in the inequality, it should be drawn as a dotted line.
Hi Selma201,
For this one, here's what I would do.
Find the x- and y-intercepts of the graph of the linear equation $\displaystyle 3x+4y=12$
To find the x-intercept, substitute 0 for y and solve for x. You should get x = 4. This means the x-intercept is (4, 0).
To find the y-intercept, substitute 0 for x and solve for y.
You should get y = 3. This means the y-intercept is (0, 3).
Plot these two points on the coordinate plane.
Since your original inequality did not have an equal sign ($\displaystyle \leq$), the line that you draw through these points will be a broken (dashed) line. This indicates that the points on the line are not part of the solution set.
Finally, pick any point above or below the line and substitute it into the original inequality. Let's choose (0, 0) which is below the line.
If the substitution makes the inequality true, shade that side of the line. If it doesn't, shade the other side.
I believe you'll find that (0, 0) is part of the solution set, so you should shade below the line which includes this point.