Answer:
graph is attached below.
Step-by-step 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.
