# What is the equation of the line passing through (3,-5) and (42,1)?

Aug 24, 2016

Both points satisfy the line equation $y = m x + b$, so you need to find $m$ and $b$

#### Explanation:

Since both points satisfy the equation, we know that:

$- 5 = m \cdot 3 + b$, and

$1 = m \cdot 42 + b$

We now have a system of two equations with $m$ and $b$. To solve it we can subtract the first from the second equation to eliminate $b$:

$6 = 39 m$ and so $m = \frac{6}{39} = \frac{2}{13}$. From the first equation now we have:

$- 5 - \left(\frac{2}{13}\right) \cdot 3 = b$, and so $b = - \frac{65}{13} - \frac{6}{13} = - \frac{71}{13}$.

The equation of the line is then:

$y = \frac{2}{13} x - \frac{71}{13}$