Question

The x-intercept of a line with a gradient (slope) of `5/6` is `-3`. What is the equation of the line in slope-intercept form?

Answer 1

The equation of the line is:

`y = 5/6x+15/6`

Explanation:

We often work with the y-intercept, but the x-intercept is less common. Still not too difficult, though.

We can write the equation of a line in standard form as:

`y=mx+c`

where `m` is the slope and `c` is the y-intercept.

We find the y-intercept by setting `x=0`, since the y-axis is the line `x=0`.

Let's see whether turning that around will work: let's set `y=0`, since the x-axis is the line `y=0`, then the value of `x` has been given to us as `-3`:

`y=mx+c`

`0=5/6(-3)+c`

Rearranging, we get:

`c=-5/6(-3)=15/6`

The overall equation of the line, then, is:

`y = 5/6x+15/6`