Question

Graph the following region--
2x-5y>=0

Answer 1

Ignoring the idea of regions, would you know how to graph 2x-5y = 0 as a line?

Answer 2

No.. I could if zero was another number. I have no examples for this kind of problem

Answer 3

The fact that the other number is 0 actually just means that you have a y-intersect of 0. Are you familiar with slope-intercept form?

Answer 4

Yes

Answer 5

Alright. So if I were to put your inequality into slope-intercept form I would have:
\(2x - 5y \ge\ 0\)

\(2x \ge\ 5y\)

\(\frac{2}{5}x \ge\ y\)

So that it maybe looks in a better order, let's rewrite this as
\(y \le\ \frac{2}{5}x\)

Now, you know slope-intercept form is \(y = mx+b\) where m is the slope and b is the y-intercept. So here we have a slope of 2/5, but no value for b. This means that the y-intercept is 0. So with that information, we can graph this line.

Would you be able to graph it given the info above?

Answer 6

Graph just the line I mean, don't worry about the region part yet.

Answer 7

Yes?

Answer 8

Just making sure :) Well, if we start from the y-intercept of 0 and use a slope of 2/5, we can get this line:

So how the line is drawn makes sense?