Write an equation of the line that passes through the given point and is perpendicular to the given line. Your answer should be written in slope-intercept form P(−6, 3), y + 3x = −14

First of all, remember what the equation of a line is:

y = mx+b
Where:
m is the slope, and
b is the y-intercept

So if we rearrange the given formula y + 3x = -14

We get y = -3x -14, where -3 is slope and -14 is y intercept

Next, we know that Perpendicular lines have opposite-reciprocal slopes, (m1 * m2 = –1 ) so the slope of the line we want to find is:

m1 = -1/m2 = -1/-3 = 1/3

Thus, y = 1/3x + b

Now to find the y intercept we can plug in our points above.

3 = 1/3(-6) + b
3 = -2 + b
b = 3 + 2 = 5

Thus, equation of the line is: y = 1/3x + 5.