Question

What is the equation of the line passing through (0, 2) and perpendicular to the line y = 4x – 3 in slope-intercept form?

Answer 1

WE have the line \[\large y=\color{green}{4}x-3\] we can use the slope of this line, "4" in finding the slope of the perpendicular line.

Answer 2

the slope of the perpendicular line is the negative reciprocal of the slope of the original. This means that \[\large \color{red}m=4 \implies -\frac{1}{\color{red}m}\]

Answer 3

Does that make sense so far?..

Answer 4

yes!

Answer 5

Awesome, so what would the slope of the perpendicular line be if you used that equation above?

Answer 6

-1/4?

Answer 7

good job!

Answer 8

Now that we've found the slope of the perpendicular line, we can use a point slope form \[\large y-\color{green}{y_{1}}=m(x-\color{green}{x_{1}}) \] and our point (0,2) to find the equation of the perpendicular line in slope intercept form

Answer 9

So we plug in our point (0,2) into the highlighted area and simplify \[\large y-\color{green}{(2)}=-\frac{1}{4}(x-\color{green}{0})\]

Are you able to simplify this? :)