# What is the equation of the line with slope  m=5/9  that passes through  (2,5) ?

##### 1 Answer
Jun 24, 2016

$y = \frac{5 x}{9} + 3 \frac{8}{9}$

#### Explanation:

There are two methods you can use.

Method 1.
Substitute m, x and y into $y = m x + c$ to find c.

$5 = \frac{5}{9} \left(2\right) + c$

$5 = \frac{10}{9} + c \text{ } \frac{10}{9} = 1 \frac{1}{9}$

$5 - 1 \frac{1}{9} = c$

$c = 3 \frac{8}{9}$

Equation: $y = \frac{5 x}{9} + 3 \frac{8}{9}$

Method 2.
Substitute m, x and y into the formula

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

$y - 5 = \frac{5}{9} \left(x - 2\right)$

$\text{ } y = \frac{5 x}{9} - \frac{10}{9} + 5$

$\text{ } y = \frac{5 x}{9} + 3 \frac{8}{9}$