Question

How do you graph `-8x+10y=40` using intercepts?

Answer 1

see explanation.

Explanation:

To find the `color(blue)" x and y intercepts"`

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

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

`x=0to10y=40rArry=4larrcolor(red)" y-intercept"`

`y=0to-8x=40rArrx=-5larrcolor(red)" x-intercept"`

Plot the points (0 ,4), (-5 ,0) and draw a straight line through them for the graph.
graph{4/5x+4 [-11.25, 11.25, -5.625, 5.625]}

Answer 2

Plug in `0` for `x` to find the `y`-intercept, and `0` for `y` to find the `x`-intercept. Then, graph these two points on a coordinate plane and connect them.

See below for the solution with graph.

Explanation:

Keep in mind that the `x`-intercept is the point where `y` is `0`, and the `y`-intercept is the point where `x` is `0`.

It's easier to remember this if you think about the intercepts on a graph `-` any point on the `y`-axis has to have an `x` coordinate of `0`, or else it wouldn't be on the `y`-axis (and vice versa).

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

First, find the `x`-intercept by plugging in `0` for `y`.

`-8x + 10(0) = 40`
`color(white)"XXXX--"-8x = 40`
`color(white)"XXXXXX.." x = -5`

The `x`-intercept, then, is `color(red)("(-5, 0)`

Next, find the `y`-intercept by plugging in `0` for `x`.

`-8(0) + 10y = 40`
`color(white)"XXXXX-"10y=40`
`color(white)"XXXXXX.."y=4`

The `y`-intercept, then, is `color(blue)("(0, 4))`

Finally, to graph the line, just graph these two points, and connect them, as shown below.