Question

Write various of the equation of a line that passes through (-6, 3) and has a slope of - 1/3

part 1:write the equation in point slope form

part 2: rewrite the equation in slope intercept form

part 3: rewrite the equation in a standard form

Answer 1

`\large\boxed{y-3=-(1)/(3)(x+6)-\text{point-slope form}}\\\boxed{y=-(1)/(3)x+1-\text{slope-intercept form}}\\\boxed{x+3y=3-\text{standard form}}`

Explanation:

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

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

m - slope

We have

`m=-(1)/(3),\ (-6,\ 3)\to x_1=-6,\ y_1=3`

Substitute:

`y-3=-(1)/(3)(x-(-6))\\\\y-3=-(1)/(3)(x+6)`

Convert to the slope-intercept form

`y=mx+b`

`y-3=-(1)/(3)(x+6)` use the distributive property

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

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

Convert to the standard form

`Ax+By=C`

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

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

`x+3y=3`