Question

What is the equation of the line that is parallel to the line y = - 1/3x + 4 and passes through the point (6, 5)?

Answer 1

`y=-(1)/(3)x+7`

Explanation:

we know that

If two lines are parallel then their slopes are equal

The equation of the given line is

`y=-(1)/(3)x+4`

the slope is
`m=-(1)/(3)`

so

the slope of the parallel line to the given line is also
`m=-(1)/(3)`

Find the equation of the line that is parallel to the given line and passes through the point (6, 5)

we have

`m=-(1)/(3)`

`point\ (6,5)`

The equation of the line in point slope form is

`y-y1=m(x-x1)`

substitute

`y-5=-(1)/(3)(x-6)`

Convert to slope intercept form

`y=mx+b`

isolate the variable y

`y-5=-(1)/(3)x+2`

`y=-(1)/(3)x+2+5`

`y=-(1)/(3)x+7`