Question

What is the graph of the inequality? 3x ≤ 2y - 7

Answer 1

( 0, 3.5) (3,8) and shaded up.

Explanation:

Given : 3x ≤ 2y - 7

To find : graph.

Solution : We have given that 3x ≤ 2y - 7

On adding both side by 7

3x + 7 ≤ 2y

On dividing by 2 both side

`(3x)/(2) + (7)/(2) \leq y`

Here slope =
`(3)/(2)` and y intercept =
`(7)/(2)`

Slope = 1 .5 and y intercept= 3.5

One point is ( 0, 3.5)

For more point by Rise over Run =
`(3)/(2)`

It mean it take 3 unit up and 2 unit right or 3 unit down and 2 unit left .

For inequality ( greater than equal to sign ) it would be shaded up.

Therefore, ( 0, 3.5) (3,8) and shaded up.

Answer 2

graph is attached below.

Explanation:

Given : equation 3x ≤ 2y - 7

We have to plot the graph for the given inequality.

Consider the given inequality 3x ≤ 2y - 7

To plot the graph we first convert inequality to equality.

then equation becomes, 3x = 2y - 7

We find the points to plot this line,

at x = 1

⇒ 3(1) = 2y - 7

⇒ 3 = 2y - 7

⇒2y = 10

⇒ y = 5

at x = 3

⇒ 3(3) = 2y - 7

⇒ 9 = 2y - 7

⇒2y = 16

⇒ y = 8

at x = 5

⇒ 3(5) = 2y - 7

⇒ 15 = 2y - 7

⇒2y = 22

⇒ y = 11

Thus, points are (1 , 5) , (3,8) and (5 , 11)

Now we plot these points and obtained the graph of line 3x = 2y -7

For region to be shaded take a test point and check whether it satisfy the given given inequality or not.

Let point be (-3, 0)

Substitute x= -3 and y = 0, we get

3(-3) ≤ 2(0) - 7

⇒ -9 ≤ - 7 (true)

Graph plot is as shown below.