Question

How to solve and graph 3x + 5y ≤ 340
I got x ≤ 0 y ≤ 68


Can you explain how to graph for me?

Answer 1

how did you end up with a "0y" in the middle?

Answer 2

I think the question just wants you to graph it, solve it for y, and then graph it. It would be easier to identify its slope and y intercept in that form.

Answer 3

yes, I agree...

you really should get the original inequality 3x + 5y ≤ 340
into a form more like a line equation: y ≤ mx + b

Answer 4

Can you explain that I ahave no idea how to do it

Answer 5

Okay, so.... write your inequality as a standard equation. Then subtract 3x from both sides, then divide by 5

Answer 6

When you get that figured out, and the equation graphed, plug in any point back into the equation. I usually use 0,0.

Answer 7

Start: 3x + 5y ≤ 340
Next, get the 3x on the right side of the inequality by subtracting 3x from both sides:
3x -3x + 5y ≤ 340 - 3x
5y ≤ 340 - 3x

Next, isolate the y term on the left side by dividing both sides by 5.
5y / 5 ≤ (340 - 3x) / 5
y ≤ (340 - 3x) / 5
y ≤ -(3/5)x + 340/5
y ≤ -(3/5)x + 68

Now, you have an inequality where you can plot the line using the slope and y-intercept.

This is essentially the same as graphing lines... it's just inequalities

Answer 8

68 is where the line crossed the y axis, and 3/5 is the slope of the line.

Answer 9

So how would the graph look ? The line would not be dotted and it would be shaded?

Answer 10

The line might be dotted, because it is less than or equal to, if it was just less than it might have to be solid. I don't know how the teacher requires it. Then you should shade the bottom part of the line, because every value that is under that line would satisfy the inequality.

Answer 11

Its required as like a full graph. With the Labeled lines, points of intersection, and axis. I also have to show the shaded solution of the three inequalities and explain what it represents.

Answer 12

I just
need to know how to graph this.

Answer 13

@LolLashae Where do you get " 3 inequalities" with only 3x + 5y ≤ 340 from your post ???

Answer 14

Now suppose: 3x + 5y = 340
-> y = ....?

Answer 15

68 is where the line crossed the y axis, and 3/5 is the slope of the line.

I just need to know how to graph that

Answer 16

Well, you need to draw the line first, then take its region:
y ≤ -3x/5 + 68

Answer 17

So you get intercept point ( 0, 68 ) and ( 5, 65), can you graph the straight line?

Answer 18

It would be two lines on the graph?

I'm sorry graphing is my weak point in math :( I have basically no idea how to do them

Answer 19

Do you know how to get the point?

Answer 20

is it with the y2-y1 and x2-x1 thing?

Answer 21

You have only ONE inequality 3x + 5y ≤ 340, so it yields ONE line!

Answer 22

ONE line makes from 2 POINTS

Answer 23

( 0, 68 ) means ( x = 0, y = 68)
means the point lies on y axis!

Answer 24

Then connect its with other point => straight line!

Answer 25

Probably the easiest way to graph this without a calculator is to take the original inequality let x = 0 , then solve for y, then let y = 0 and solve for x.

3x + 5y ≤ 340 original equation

3x + 5y ≤ 340 let x = 0
3*0 + 5y ≤ 340
5y ≤ 340 divide both sides by 5
y ≤ 340/ 5
y ≤ 68 this means the y-intercept is y = 68 and the graph is shaded BELOW y = 68.


3x + 5y ≤ 340 original equation

3x + 5y ≤ 340 let y = 0
3x + 5*0 ≤ 340
3x ≤ 340 divide both sides by 3
x ≤ 340/3
x ≤ 113.3 repeating Or x ≤ 113 + 1/3

That means your x intercept is 113.3 repeating and the graph is shaded to the LEFT of x = 113.3 repeating.

If you go to wolframalpha.com and type

3x+5y<= 340

You'll see exactly that. :)

Answer 26

Thank you