Question

What is the slope and intercept for `2x+3y=9` and how would you graph it?

Answer 1

`m=-2/3`

`c=9`

Explanation:

A straight line graph is of the form:

`y=mx+c`

`m` is the gradient

`c` is the intercept which is the point at `x=0` where the line cuts the `y` axis.

So we get our equation into this form:

`2x+3y=9`

`3y=-2x+9`

`y=-2/3x+9`

So the slope or gradient `m=-2/3`

The intercept `c=9`

To graph it manually just pick a range of values of `x` and find the corresponding value of `y`.

e.g `x=1rArr`

`y=-(2/3xx1)+9= =25/3`

So your 1st point is `[1,25/3]`

You should end up with this:

graph{-2/3x+9 [-16.5, 23.5, -8.7, 11.3]}