Question

Write the equation of the line that passes through the given point and has the given slope. (-12,5)

slope = 1/3

Answer 1

`_{\text{point-slope form}}`

`\huge\boxed{y-5=(1)/(3)(x+12)}`

`_{\text{slope-intercept form}}`

`\huge\boxed{y=(1)/(3)x+9}`

`_{\text{standard form}}`

`\huge\boxed{x-3y=-27}`

Explanation:

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

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

where

`m` - slope

`(x_1;\ y_1)` - a point on a line

We have

`m=(1)/(3);\ (-12;\ 5)\to x_1=-12;\ y_1=5`

Substitute:

`y-5=(1)/(3)(x-(-12))\\\\y-5=(1)/(3)(x+12)\\==================`

`y-5=(1)/(3)(x+12)\qquad|\text{use the distributive property}\ a(b+c)=ab+ac\\\\y-5=(1)/(3)x+4\qquad|\text{add 5 to both sides}\\\\y=(1)/(3)x+9\\=======================`

`y=(1)/(3)x+9\qquad|\text{multiply both sides by 3}\\\\3y=x+27\qquad|\text{subtract}\ x\ \text{from both sides}\\\\-x+3y=27\qquad|\text{change the signs}\\\\x-3y=-27`

Answer 2

Answer: y= 1/3x + 41