I need help asap!!! -3x+2y>4. I have to describe the inequality and graph the region (shade).?

Question

If you could answer and briefly explain I would be so grateful!!!

Answer 1

You need to get y by itself.

add -3x to both sides so you get 2y> 3x+4
now divide 2 --> y>3/2x+2

graph that as you would if it were y=3/2x+2
(starting at 2 on the y axis. then move up 3 points, and 2 to the right.)

Make sure your line is DOTTED. It is only solid if the inequalilty is less/greater than or equal to.

to check which side is to be shaded, plot points on both sides. try (0,0) if the line doesn't cross through that.

:)

If the answer is correct, shade the region where (0,0) or the coordinates that work are.

Answer 2

Since you have two variables, your graph will be a line on a coordinate grid. I would recommend solving for y in terms of x giving us what's known as the slope-intercept form of the equation.

2y > 3x + 4
y > (3/2)x + 2

Thus, (0, 2) is the y-intercept and the slope is 3/2. This is also known as rise over run. You can go up 3 units and over 2 to the right and another point on the line is (2, 5). The line would be most correctly sketched using a dashed line since this is a strict inequality.

After drawing the line, check a point on either side. Choosing the origin , (0, 0), is the easiest. The statement is not true when x and y both equal 0 so shade to the right of the line.

Answer 3

To graph this ignore the ">" sign for a moment and just graph the line -3x+2y=4. Now pick a random point on either side of the line [(0,0) is a good one] and plug the x and y coordinates into the original inequality. For example, plug in (x,y)=(0,0) and you'll get -3(0)+2(0)>4. Is this true? If it is, shade in the area to the side of the line that includes (0,0). If this is false, shade in the side of the line that does not include (0,0).

Edit: Oh yeah, kudos to Gwen, don't forget to make your line -3x+2y=4 a dotted line.

Answer 4

First, graph the equation as if the less than sign is an equals sign. Second, pick a point, any point, on either side of the line. (Often (0,0) is the easiest one to use.) Enter the coordinates of this same point into the equation, with the original less-than sign. If the equation is valid for the point, shade the side of the line(or curve) that includes the point. If not, shade the other side of the line (or curve).

Answer 5

-3x+2y>4
add 2x to both sides
2y>3x+4
dividing by 2
y>(3x+4)/2
now find the ordered pairs as though y=(3x+4)/2
draw the line and shade the portion above the line

Answer 6

i think you would have to put -3x+2y in y-form.

-3x+2y>4

-3x+2y=0

2y=3x

y=3/2x

you graph it from using 3/2 as your slope. graph it from point zero. since your equation was -3x+2y>4, then you shade the top region.