Answer
Option 2
Explanation:
Given the following inequality
[tex]-9x\text{ + 4y }\leq\text{ 8}[/tex]Step 1: Turn the inequality to an equation
The inequality becomes
-9x + 4y = 8
Step 2: find the x and y - intercepts
To find the y - interecpts, make x = 0
-9x + 4y = 8
make x = 0
-9(0) + 4y = 8
0 + 4y = 8
4y = 8
Divide both sides by 4
4y/4 = 8/4
y = 2
When x = 0 y= 2 ------------------- (0, 2)
Find x - intercept
Make y = 0
-9x + 4y = 8
-9x + 4(0) = 8
-9x + 0 = 8
-9x = 8
Divide both sides by -9
-9x / -9 = 8/-9
x = -8/9
x = - 0.888
Therefore, x = -0.888 or -8/9 when y = 0
(-8/9, 0)
Step 3: Graph the points
Therefore, the answer is option 2
The straight line is thick because the inequality sign is is less than or equal to
Also, the inner part of the graph was shaded because the function is less than or equal to the point
