Question

What are the intercepts of `-6y-2x=5`?

Answer 1

`-2.5` or `-5/2`

Explanation:

Solve the equation for y:
`-6y - 2x = 5`
`-6y = 5-2x`
`y=((5-2x)/-6)`
Set the equation equal to zero in order to find the y values that are 0 which are the intercepts
`0 = ((5-2x)/-6)`
In order to get a fraction equal to 0, only the numerator needs to equal 0 so we can ignore the denominator
`0=-5-2x`
`5= -2x`
`5/-2 = x`
Intercept at `(-5/2,0)`

Answer 2

Finding the X-intercept:

Plug `0` in for `y`.

What this does, in effect, is causes the `-6y` term to disappear.

`color(red)(cancel(color(black)(-6y)))-2x=5`

`-2x=5`

`x=-5/2`

Thus, if `x=-5/2` and `y=0`, the point of the `x`-intercept is `(-5/2,0)`.

Finding the Y-intercept:

Similar to the previous example, plug in `0` for `x`. An easy way to think about this is just covering up `-2x` with your finger.

`-6ycolor(red)(cancel(color(black)(-2x)))=5`

`y=-5/6`

Which gives us a `y`-intercept of `(0,-5/6)`.

A graph of the line can help to confirm your answers:

graph{-(2x+5)/6 [-10, 10, -5, 5]}

The point where the line crosses the `x`-axis (the `x`-intercept) is `(-2.5,0)`, which equals `(-5/2,0)`.

The `y`-intercept on the graph is `(0,-0.833)`, which is equivalent to `(0,-5/6)`.