# How do you write an equation for a line that is parallel to y=3x+7 and passes through (2,10)?

Nov 20, 2016

$y = 3 x + 4$

#### Explanation:

$y = m x + b$

Where $m$ is the slope and $b$ is the y intercept

The slope of the given equation, $y = 3 x + 7$ is $3$

So, to write an equation parallel to the given equation and set of points, use point slope form and the slope of $3$:

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

Where $\left(2 , 10\right) \implies \left({x}_{1} , {y}_{1}\right)$ and $m = 3$

$y - 10 = 3 \left(x - 2\right)$

Distribute the $3$ throughout the set of parenthesis

$y - 10 = 3 x - 6$

Perform the opposite operation to isolate $y$ by adding $10$ on both sides of the equation

$y = 3 x + 4$

As you can see, the slope of this line is $3$, which means that the two equations are parallel to each other