# How do you write an equation of a line given (0,4) and m=2?

Oct 5, 2016

$y = 2 x + 4$

#### Explanation:

We use the point-slope form:
$y - {y}_{1} = m \left(x - {x}_{1}\right)$
where ${x}_{1}$ and ${y}_{1}$ are the coordinates of a point on the line and $m$ is the slope of the line. Given (0, 4) and $m = 2$, we get:
$y - 4 = 2 \left(x - 0\right)$
This immediately simplifies to:
$y - 4 = 2 x$
Isolating $y$ gives the equation of the line in slope-intercept form:
$y - 4 + 4 = 2 x + 4$
$y = 2 x + 4$
Since the question does not specify which form of a linear equation is required, it is customary to give the answer in slope-intercept form.