How do you graph `2x+5y=10` using intercepts?

The equation of a straight line with gradient `m` and `y`-intercept `c` is:

`y=mx+c`

You have been given all the information you need but to get to this format, need to rearrange:

`2x+5y=10`

subtracting `2x` from each side gives

`-2x+2x+5y=10-2x`

`5y=-2x+10`

Dividing through both sides by `5` gives

`(5y)/5=(-2x)/5+10/5`

`y=-2/5x+2`

So now it can be seen that the `y`-intercept is `2` and the gradient is `-2/5`.

The `x`-intercept can be found when `y=0`:

`0=-2/5x+2`

To find the value of `x` this again needs rearranging:

`0+2/5x=-2/5x+2+2/5x`

`2/5x=2`

`2/5x xx5/2=2xx5/2`

`x=10/2=5`

So the `x`-intercept is at `5`.

This means that the graph will cross through:

the `x`-intercept `(0,5)`; and

the `y`-intercept `(2,0)`.

You can mark these on your graph and then draw a line through them both.

Graph of `y=-2/5x+2`
graph{-2/5x + 2 [-7, 7, -7, 7]}

To find the intercepts.

`• " let x = 0, in the equation, for y-intercept"`

`• " let y = 0, in the equation, for x-intercept"`

`x=0to0+5y=10toy=2larrcolor(red)" y-intercept"`

`y=0to2x+0=10tox=5larrcolor(red)" x-intercept"`

Plot the points (0 ,2) , (5 ,0) and draw a straight line through them. This is the graph of 2x + 5y = 10
graph{-2/5x+2 [-10, 10, -5, 5]}