Question

Which is an equation of the line that passes through the point (0, 4) and is perpendicular to the line whose equation is y = −12x + 3?

Answer 1

Since the line that we need to figure out is perpendicular to the one given, the slope of the line in question is going to be the opposite-reciprocal of the slope of the given line.

Slope of the given line = -12

Slope of the new line =
`(1)/(12)`

We will use the point given and the new slope to determine the y-intercept using slope-intercept form.

`4 = (1)/(12)(0) + b\\\\4 = 0 + b\\\\4 = b`

Formula for this line

`y = (1)/(12)x + 4`

We can graph the lines to check our work.

Both lines are perpendicular.