# How do you write an equation of the line that has slope 2/3 and passes through point (-6, 4)?

Oct 9, 2015

The equation you are looking for is: $y = \frac{2}{3} x + 8$

#### Explanation:

In the general equation of a line: $y = a x + b$ $a$ is the slope, so the equation we are looking for can be written as: $y = \frac{2}{3} x + b$. Now we have to find such value for $b$ to satisfy the second condition (line passes through (-6,4)). To do this we have to substitute $- 6$ for $x$ and $4$ for $y$.

$4 = \frac{2}{3} \cdot \left(- 6\right) + b$

$4 = - 4 + b$

$b = 8$

Answer: The line has equation: $y = \frac{2}{3} x + 8$