Question

What is the equation of a line, in point-slope form, that passes through (−2, −6) (−2, −6) and has a slope of  1/3?

Answer 1

Answer:

$y+6=\frac{1}{3}(x+2)$

Step-by-step explanation:

General equation of point slope form : $y-y_1=m(x-x_1)$

where m is the slope

Point = $(x_1,y_1)=(-2,-6)$

Slope = $m = \frac{1}{3}$

Substitute the values in general form of point slope form .

$y-y_1=m(x-x_1)$

$y-(-6)=\frac{1}{3}(x-(-2))$

$y+6=\frac{1}{3}(x+2)$

This can be simplified further

$y+6=\frac{1}{3}x+\frac{2}{3}$

$y=\frac{1}{3}x+\frac{2}{3}-6$

$y=\frac{1}{3}x-\frac{16}{3}$

Hence the equation of a line, in point-slope form, that passes through (−2, −6) and has a slope of  1/3 is $y+6=\frac{1}{3}(x+2)$

Answer 2

Point-slope form is y - y1 = m(x - x1)

plug in the given slope and the given point

y - (-6) = (1/3)(x - (-2))

then simplify

y + 6 = (1/3)(x + 2)