# What is the slope of 5y=1/3x+1?

Mar 13, 2018

The slope is $\frac{1}{15}$
The intercept is $\frac{1}{5}$

#### Explanation:

To make progress it is necessary to write the equation of the line in the form

$y = m x + c$

where $m$ is the slope and $c$ is the intercept.

By inspection, you might note that division of $5 y$ by $5$ will put the left hand side of the equation in a suitable form to compare it with the conventional slope-intercept form shown above. Remember that it will also be necessary to divide (every term in the) right hand side by $5$

That is,

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

implies

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

that is

$y = \frac{1}{15} x + \frac{1}{5}$

This is now in a suitable form to compare with $y = m x + c$

By inspection,

$m$ corresponds to $\frac{1}{15}$ so this is the slope
and
$c$ corresponds to $\frac{1}{5}$ so this is the intercept