# How do you write the equation of a line in point slope form that is parallel to y=2/3x+9 and goes through (4,8)?

May 14, 2015

The answer is $y = \frac{2}{3} x + \frac{16}{3}$

The function we are looking form is a linear function, so it can be written as $y = a x + b$.
The line is parallel to $y = \frac{2}{3} x + 9$ so $a = \frac{2}{3}$ (If 2 lines are parallel their $a$ coefficients are equal).
Now we have to calculate $b$ knowing that the line goes through $\left(4 , 8\right)$ so you can substitute 4 for $x$ and 8 for $y$ and solve the equation for $b$.

The equation is $8 = \frac{2}{3} \cdot 4 + b$, so $b = 8 - \frac{2}{3} \cdot 4$
$b = \frac{24}{3} - \frac{8}{3}$
$b = \frac{16}{3}$

So the final answer is $y = \frac{2}{3} x + \frac{16}{3}$