# How do you write an equation of a line going through (2,8) parallel to y=3x-2?

Aug 21, 2017

See a solution process below:

#### Explanation:

the equation in the problem is in slope-intercept form. The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

Therefore $y = \textcolor{red}{3} x - \textcolor{b l u e}{2}$ has slope: $\textcolor{red}{m = 3}$

Because the lines are parallel, by definition, the two lines will have the same slope.

We can substitute the slope into the equation to begin writing the equation for the line going through point $\left(2 , 8\right)$

$y = \textcolor{red}{3} x + \textcolor{b l u e}{b}$

We can now substitute the values from the point in the problem for $x$ and $y$ in the equation we started writing and solve for $\textcolor{b l u e}{b}$:

$8 = \left(\textcolor{red}{3} \cdot 2\right) + \textcolor{b l u e}{b}$

$8 = 6 + \textcolor{b l u e}{b}$

$- \textcolor{red}{6} + 8 = - \textcolor{red}{6} + 6 + \textcolor{b l u e}{b}$

$2 = 0 + \textcolor{b l u e}{b}$

$2 = \textcolor{b l u e}{b}$

$\textcolor{b l u e}{b} = 2$

We can now substitute $2$ for $\textcolor{b l u e}{b}$ in the equation we started to write the complete equation:

$y = \textcolor{red}{3} x + \textcolor{b l u e}{2}$