Question

How do you graph `-10x+15y=60` using intercepts?

Answer 1

See a solution process below:

Explanation:

x-intercept

To find the `x`-intercept we set `y` to `0` and solve for `x`:

`-10x + (15 * 0) = 60`

`-10x + 0 = 60`

`-10x = 60`

`(-10x)/color(red)(-10) = 60/color(red)(-10)`

`(color(red)(cancel(color(black)(-10)))x)/cancel(color(red)(-10)) = -6`

`x = -6` or `(-6, 0)`

y-intercept

To find the `y`-intercept we set `x` to `0` and solve for `y`:

`(-10 xx 0) + 15y = 60`

`0 + 15y = 60`

`15y = 60`

`(15y)/color(red)(15) = 60/color(red)(15)`

`(color(red)(cancel(color(black)(15)))y)/cancel(color(red)(15)) = 4`

`y = 4` or `(0, 4)`

We can now plot the two points and draw a line through them to graph the equation:

graph{((x+6)^2+y^2-0.025)(x^2+(y-4)^2-0.025)(-10x+15y-60)=0}