Question

Which shows the graph of the solution set of 2x + 3y ≤ 6?

Answer 1

Answer:

option A

Step-by-step explanation:

2x + 3y ≤ 6

To graph the given inequality, we replace <= symbol by =

2x + 3y = 6

Solve for y, subtract 2x on both sides

3y= -2x+6

now divide both sides by 3

$y=\frac{-2}{3}x+2$

Now we make a table, assume some numberrs for x  and find out y

x        y= -2/3x + 2

-3        y= (-2/3)(-3)+2= 4

0          y=2

3           y=0

Use point (-3,4)  (0,2)  and (3,0) for graphing. Used solid line

Now shading, use test point (0,0)

2x + 3y ≤ 6

2(0) + 3(0)<=6

0<=6  that is true so we shade the part that contains (0,0)

The graph is attached below

Answer 2

The dividing line will have to hit the points (0,2) and (3,0)
then you can test the point (0,0) which satisfies the inequality, so you will shade the side that has (0,0) on it, so it's the first picture.