Question

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)`?

Answer 1

`3y=x+1`

Explanation:

The slope of this line is `-3`. Slope of a line perpendicular to it it `1/3`.
Because `m_1*m_2=-1` where `m_1` and `m_2` are the slope of perpendicular lines

Now, the equation of the line is `y=x/3+c`

To find `c`, put a point which in this case is `(1,2/3)`

`2/3=1/3+c` `=>` We get that `c=1/3`

So required equation is `y=x/3+1/3` or `3y=x+1`