Question

Alda graphed the linear function 3y = - 12 + 3x below. If she graphed the function correctly,

explain how you know that. If she graphed the function incorrectly, explain what she did wrong and
what the correct graph should look like.
124
1-11
-
10
100
1-12-11
10
9
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
11 12
TY
--11
- 12​

Answer 1

The given function is

`3y=-12+3x`

There's no graph. But we can find the right one.

To graph a linear equation, we just need to find two points only, the y-intercept point and the x-intercept point.

Y-Intercept: For
`x=0`, let's find
`y`

`3y=-12+3x\\3y=-12+3(0)\\3y=-12\\y=-(12)/(3)\\ y=-4`

That means the y-intercept is at
`(0,-4)`.

X-Intercept: For
`y=0`, let's find
`y`

`3y=-12+3x\\3(0)=-12+3x\\0=-12+3x\\12=3x\\x=(12)/(3)\\ x=4`

The x-intercept is at
`(4,0)`

The next step is to graph both coordinates and draw line that intercept them, as the image attached shows, observe the axis interception points.

So, you must have a line like the one we show in the image.