passes through (-1,-8) and perpendicular to x+ 3y = -6

Question

using point slope formula

how do you find the slope formula

Answer 1

Hi Leilanny!

Point-slope form is one way in which we can write an equation for a line. In general, point slope formula is

(y-y_o) = m*(x-x_o)

where m is the slope, and (x_o,y_o) is a point that the line passes through.

So, first order of business is to find the slope of the given line. Let's put that equation into slope-intercept form. We have

x + 3y = -6

subtract x from both sides

3y = -x - 6

divide by 3

y = -x/3 - 2

Which is in slope intercept form. Evidently, the slope of the given line is -1/3.

So our line, which is perpendicular, must have a slope that is the negative reciprocal of the given line.

So,

m = 3

So, in point-slope form, using (x_o,y_o)=(-1,-8) and m = 3, the equation of the line is

y + 8 = 2 (x + 1)