Question

Write an equation of the line that goes through the point (3,7) and is perpendicular to the line y=-3x + 6 .

Answer 1

hmmm what's the slope of -> y=-3x + 6 <-- anyway?

Answer 2

The slope is -3

Answer 3

yes, the slope is -3
the slope of a perpendicular line to this one is -1/m
where m is the original slope (-3 in this case)

I don't know a quick way to derive this fact, so you just have to remember it (if you want to do these problems)

Answer 4

now you have a problem of finding the equation of a line given
that you know its slope = ⅓ and it goes through the point (3,7)

use
\[ y - y_0 = m(x-x_0) \]
where m is the slope and \( (x_0,y_0) \) is the known point.
after you put in the numbers, you can rearrange to slope-intercept form if you like.