Question

Graph the linear inequality: 2x + 3y = 12, by creating a t-chart to plot the points. Shade by

testing a point and show all of your work

Answer 1

See explanation

Explanation:

Assuming the given inequality is
`2x+3y\le12`

Then the corresponding linear equation is
`2x+3y=12`

When x=0, we have
`2*0+3y=12`

`\implies 3y=12\implies y=4`

When y=0, we have
`2x+3*0=12`

`\implies 2x=12\implies x=6`

The T-table is:

x | y

0 | 4

6 | 12

We plot this points and draw a solid straight line as shown in the attachment.

Now let us test the origin: (0,0) by plugging x=0 and y=0 into the inequality.

`2*0+3*0\le12`

`0\le12`....This is true so we shade the lower half plane as shown in the attachment.