Question

How do you find the x and y-intercept given `y= 4x - 7`?

Answer 1

x-intercept = `7/4`
y-intercept = `-7`

Explanation:

There is a very standard way to solve such problems. Let us take an equation of a line in standard form: `y = m x + c`, where `m` is the slope and `c` is the y-intercept.

Firstly, get all the variables to the left-hand side (LHS) and the constant to the right-hand side (RHS). So, we get:
`-m x + y = c`

Now divide the whole equation by the constant on the RHS (note that this does not change the equation), and write it in the form below:
`-m x/c + y/c = 1` (Dividing by `c`)
`x/(-c/m) + y/c = 1` (Dividing by `c`)

In this form, the term below `x` (here: `-c/m`) gives the x-intercept and the term below `y` (here: `c`) gives the y-intercept.

Let us turn our attention to the question given. We have:
`y = 4x - 7`
`=> 4x - y = 7`
`=> x / (7/4) + y / (-7) = 1`
Thus the x-intercept is `7/4` and the y-intercept is `-7`.