I have a question on math homework. Graphing to be specific?

Question

Sketch the graph of inequailty.

3x - 2y < 6.

Do I have to work out the problem or can I just graph it from there?
If I DO have to work out the problem, how do you solve it?

Answer 1

you need to get y one side.
3x-2y<6
-3x -3x

-2y<-3x+6
/-2 /-2

y>(3/2)x -3

Answer 2

When graphing, I like to get x or y by itself (preferably y):
3x - 2y < 6 ... Subtract 3x from both sides...
-2y < 6 - 3x ... Divide both sides by -2 (remember to flip the '<' sign when multiplying or dividing by a negative number) ...
y > -3 + (3/2)x ... or ...
y > (3/2)x - 3

Then from here, I usually make a graph:
| x | y |
| 0 |-3|
| 2 | 0 |
|-2 | -6|

Now you have three points to plot: (0, 3), (2, 0), and (-2, -6).

Remember to use a dotted line, and to test which side to "shade", I pick a point, such as (0, 0) (as long as the point is NOT on the line, it can be a test point). Now take the point and stick it into the equation:

y > (3/2)x - 3
0 > (3/2)(0) - 3
0 > -3 ... Which is true, so shade the section that contains point (0, 0).

Hope that helps you understand...

Answer 3

You can graph it on certain calculators if you solve for y. If graphing by hand, first solve for y,
3x-2y<6
-2y<-3x+6
y>(3/2)x-3

(switch inequalities when dividing or multiplying by a neg)

then pretend it is an equal sign and graph (with a dotted line because it is a less than and not an equal to). After you have graphed, check points on each side of the line for shading. If the point works shade that side if it does not shade the other.

Answer 4

stressful to coach a graph, yet i'm able to describe the thank you to get there. Ralph made 3 money and owes $500. After 5 greater money, he nevertheless owes $250. this means that Ralph paid $250 in 5 months, or $50/month, so he paid $a hundred and fifty finished contained in the 1st 3 months. His preliminary very own loan became into $650. On a graph, label the Y-axis with the greenback quantity owed in $50 increments (0, $50, $one hundred, $a hundred and fifty, and so on.). Label the X-axis with time in months (0, a million month, 2 months, 3 months, and so on.) on the graph, mark your 2 customary factors ($500,3) and ($250,8). utilizing a ruler, connect those factors and proceed the line via the two the x and y axis. the place the line crosses the y-axis, that's the quantity owed at time t=0, or the preliminary very own loan quantity. the place the line go the x-axis, that's the month the place not greater money is owed, or the size he has the non-public loan. when you consider that we calculated the fee for the preliminary very own loan ($650) you need to use this to envision your graph.

Answer 5

Solve the problem for y as if the < were an =
y>-3-3/2x (remember the inequality flips when you divide or multiply by a negative.)

Now graph the line and the shading goes above the line because y is greater than the x part.

Answer 6

3x-2y<6
= 3x<6+2y
= 3x-6<2y
= 3/2x -3

Answer 7

3x-2y=0
3x=2y
x=2y/3
x=0,y=0
x=6 y=9
x=2 y=3
now with these ordered pairs draw thw line and shade the portion below it
that will be 3x-2y<6

Answer 8

probably you should make the equation into the form

y > mx + b.
so for your equation

y >3/2x -3

put on some values of x to get the corresponding value for y.

since y > , you have to shade the portion of the graph that's
right above the y axis for emphasis...

there ya go...

Answer 9

solve for y, then enter it as normal

on your calculator highlight the "=" sign and hit the enter button and it will change symbols until it shows the correct one and graph it. It will shade it and everything for you.

Answer 10

You need to get y by itself so it would be
y> 3/2x-3
Then you can graph it from there...