# How do you write an equation in slope-intercept form for a line that is parallel to the given line y = 1/3x + 5 and passes through the given point(0,-5)?

Jul 3, 2015

$y = \frac{1}{3} x - 5$

#### Explanation:

As you might know, lines that are parallel have the same value at $x$, in this case $\frac{1}{3}$. This is because this represents the slope of the line, and same slope means parallel lines.
To get the full equation, there is a formula, but there's also a way if you don't know the formula. Let's do it without the formula first:

Without the formula
Let's write down what we know of our function at the moment:
$y = \frac{1}{3} x + c$
All we need to know is $c$. Since we know one of the points, we can just replace the $x$ and $y$ value and solve for $c$:
$- 5 = \frac{1}{3} \cdot 0 + c$
$c = - 5$
It's that easy! The equation is thus:
$y = \frac{1}{3} x - 5$

With the formula
The formula to find the equation of a line through a given point and with a given slope is:

$y - y 1 = m \left(x - x 1\right)$
where $y 1$ is the $y$-value of your point, $x 1$ the $x$-value and $m$ the slope.
In this case, it will be:
$y - \left(- 5\right) = \frac{1}{3} \left(x - 0\right)$
$y + 5 = \frac{1}{3} x$
$y = \frac{1}{3} x - 5$