Question

How do you find the x and y intercepts for `5x -2y -6 =0`?

Answer 1

x-intercept `(6/5, 0)`
y-intercept `(0,-3)`

Explanation:

The way to find intercepts is simple. All we need to do is first set one variable to zero. Let say we start with `y=0` then solve for the x-intercept. After which, set `x=0` then solve for y-intercept.

Let us do it.

`5x-2y-6=0`

Set `y=0` from the original equation

`5x-2y-6=0`

`5x-2(0)-6=0`

`5x-0-6=0`

`5x=6`

`(5x)/5=6/5`

`(cancel5x)/cancel5=6/5`

`x=6/5=1.2`

Now, Set `x=0` in the original equation `5x-2y-6=0`

`5(0)-2y-6=0`

`0-2y-6=0`
`-2y=6`

`(-2y)/(-2)=6/(-2)`

`(cancel(-2)y)/cancel(-2)=6/(-2)`

`y=6/(-2)`

`y=-3`

Kindly see the graph of `5x-2y-6=0`
We can see that the line intersects with the axes at `(6/5, 0) and`(0, -3)#

graph{5x-2y-6=0[-20,20,-10,10]}

God bless....I hope the explanation is useful.