# How do you write an equation in slope-intercept form for an equation of a line perpendicular to y = -3x +1 and that intersects at point (1, 2/3)?

Mar 29, 2018

$3 y = x + 1$

#### Explanation:

The slope of this line is $- 3$. Slope of a line perpendicular to it it $\frac{1}{3}$.
Because ${m}_{1} \cdot {m}_{2} = - 1$ where ${m}_{1}$ and ${m}_{2}$ are the slope of perpendicular lines

Now, the equation of the line is $y = \frac{x}{3} + c$

To find $c$, put a point which in this case is $\left(1 , \frac{2}{3}\right)$

$\frac{2}{3} = \frac{1}{3} + c$ $\implies$ We get that $c = \frac{1}{3}$

So required equation is $y = \frac{x}{3} + \frac{1}{3}$ or $3 y = x + 1$