Question

Which equation represents a line that has a slope of 1/3 and passes through the point (–2, 1)?

Answer 1

Explanation:

The pointl-slope form of an equation of a line:

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

m - slope

We have

`m=(1)/(3),\ (-2,\ 1)\to x_1=-2,\ y_1=1`

Substitute:

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

`y-1=(1)/(3)(x+2)` → the point-slope form

Convert to the slope-intercept form:

`y-1=(1)/(3)(x+2)` use the distributive property

`y-1=(1)/(3)x+(2)/(3)` add 1 = 3/3 to both sides

`y=(1)/(3)x+(5)/(3)` → the slope-intercept form

Convert to the standard form:

`y=(1)/(3)x+(5)/(3)` multiply both sides by 3

`3y=x+5` subtract x from both sides

`-x+3y=5` change the signs

`x-3y=-5` → the standard form

Convert to the general form:

`x-3y=-5` add 5 to both sides

`x-3y+5=0` → the general form