# Given the equation y − 3 = 1/5(x + 6) in point-slope form, how do you identify the equation of the same line in slope-intercept form?

Change the equation to the form of $y = m x + b$ to arrive at
$y = \frac{1}{5} x + \frac{21}{5}$

#### Explanation:

We're changing the form of the equation from point-slope to slope-intercept. To do this, first solve for y:

$y - 3 = \frac{1}{5} \left(x + 6\right)$
$y = \frac{1}{5} \left(x + 6\right) + 3$

Next we're going to change the format of the right side of the equation so that it has the form of $m x + b$ where m is the slope and b is the y-intercept. To do that, first distribute the 1/5:

$y = \frac{1}{5} x + \frac{6}{5} + 3$

Since there is only the one x term, $m = \frac{1}{5}$. So now we just need to clean up the y-intercept:

$y = \frac{1}{5} x + \frac{6}{5} + 3 \cdot \frac{5}{5}$

$y = \frac{1}{5} x + \frac{6}{5} + \frac{15}{5}$

$y = \frac{1}{5} x + \frac{21}{5}$

And that's the answer in the format of $y = m x + b$