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

Jul 27, 2015

x-intercept = $\frac{7}{4}$
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:
$- m \frac{x}{c} + \frac{y}{c} = 1$ (Dividing by $c$)
$\frac{x}{- \frac{c}{m}} + \frac{y}{c} = 1$ (Dividing by $c$)

In this form, the term below $x$ (here: $- \frac{c}{m}$) 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:
$y = 4 x - 7$
$\implies 4 x - y = 7$
$\implies \frac{x}{\frac{7}{4}} + \frac{y}{- 7} = 1$
Thus the x-intercept is $\frac{7}{4}$ and the y-intercept is $- 7$.