The graph of the inequality 2x – y + 4 > 0 is the shaded region which:?

Question

a. is above the line whose intercepts are (0, 4) and (–2, 0).

b. is to the right of the line whose slope is 2.

c. doesn't include the origin.

d. includes the points (3, 5), (2, –1), and (1, 6).


AND:

The graph of y > x – 1 is the shaded region which is located:

a. to the right of the vertical line x = 1

b. to the left of the line x = y + 1

c. above the line y = x + 1

d. to the right of the line y = x – 1

Answer 1

I think this is your assignment. So I will do only one problem and the other is just same as the first one.

So you only try the second one to get the concept.

CONCEPT :
The main concept in this type of problemsis as follows
1. First find the intercepts of the inequation as an equation by replacing the < or > symbol to =.
2. Find the intercepts.
3. This is the important job. I think you know how to find out the slope of the line. So if the slope is negative then the inequation with > sign will be shaded in the above region and < sign will be shaded in the below region and it is reverse in the case when the slope is positive.
4. Now the job is finished and you can choose the right option.

I am doing the first one for your understanding.
Given equation is 2x – y + 4 > 0
Finding the intercepts by changing the > sign to =.
2x - y + 4 = 0
gives 2x - y = -4
Dividing with -4 in both sides
gives x/(-2) + y/4 = 1
This is in the form, x/a + y/b = 1, where a and b are x and y intercepts respectively.

Therefore the intercepts are (-2,0) and (0,4)

Slope of the line is positive and the sign is '>'. So the shaded region should be below the line.

The first option is wrong because the region will be below the got intercepts.

The second option is wrong as the slope of the line is 2.

The third option is wrong as you can find the origin in the shaded region. You can check in the graoh also.

For the 4th option, checking each point,
(3,5) gives 2(3)-5+4 > 0 which is true.
(2,–1) gives 2(2) - (-1)+4 > 0 which is true.
(1, 6) gives 2(1) - 6 +4 >0 which is false. (0 is not > 0)

So all the options are wrong. The fourth option will be correct if the given inequation has greater than or equal to sign.

I think I had explained very much indetail because I think you are somewhat not upto the mark in this kind of sums. So follow the concept to get the subject.

Similarly you can do the other sum also Please try. If you dont get, then I will help you if you contact me.

Answer 2

When I was your age I used to solve this stuff as follows.
First I made an equation from the inequality :
2x - y + 4 > 0 => y = 2x + 4.

Next I took a paper and drew the line y = 2x + 4
x = 0 gives y = 4, x = 1 gives y = 6 thus the line goes through (0,4), (1,4).

Now all the points below the line have y-values smaller
2x + 4 ( y < 2x + 4 ) are below the line.

points on the line have y values equal to 2x + 4 ( y = 2x + 4 )

points above the line have y values greater than 2x + 4.

since "they" asked to shade the area for 2x - y + 4 >0 ( or that is the same 2x + 4 > y )
you have to take the points below the line. SHADE IT,

then verify each of the alternative a), b), c), d) and choos te right one.

Answer 3

First write the equation in terms of y as a function of x
y<2x + 4
Analysis
let x=0 then y<4 and
let y=0 then 0<2x+4 or x>-4/2= - 2
If you sketch the line y=2x + 4 you can clearly see the the values lie to the right of the function y=2x + 4. And the intercepts y<4 at x=0 and x>-2 at y=0 suggest that as well.

Answer 4

Y<2x+4