# How do you write an equation in slope intercept form given a slope and a x-intercept?

Dec 22, 2014

What is x-intercept? It is such an argument (x-value) where y-value equals 0. In equations you would tell that it is root of the equation.

In general formula $y = m x + b$ you insert known information, where $m$ is a slope (or gradient) and $b$ is free-term (or y-intercept - such an value where function cuts y-axis, so point (0, b) ).

Let us take example. You are given slope - it is 2. And you know that your x-intercept is equal 3. Therefore, you know that when $x = 3$, $y = 0$.

Let us use that information. You know that you may write every linear function like that: $y = m x + b$.
Let us insert values: $0 = 2 \cdot 3 + b$
Our unknown is $b$, free term. Let us isolate it:
$b = - 6$.
And after all, we must insert our $b$ value back into equation: $y = 2 x - 6$.