# How do you write an equation of the line with slope 3/7 containing the point (3,8)?

Nov 8, 2015

$y = m x + b$

We already know the slope, what remains is to find the $y$-intercept. To find the $y$-intercept, simply plug-in any known value for $x$ and $y$.

$\implies y = \frac{3}{7} x + b$
$\implies 8 = \frac{3}{7} \left(3\right) + b$
$\implies 8 = \frac{9}{7} + b$
$\implies 56 = 9 + 7 b$
$\implies 47 = 7 b$
$\implies \frac{47}{7} = b$

Hence, the equation of the line is

$y = \frac{3}{7} x + \frac{47}{7}$