Question

What is the equation of the line with slope `m= 1/3` that passes through `(-7/15,-5/24)`?

Answer 1

`y=x/3-19/360`

Explanation:

`y=mx+c`

`-5/24=1/3 * (-7/15) + c`

`c=-5/24+1/3*7/15`

`c=-19/360`

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Let the desired equation be

`y=mx+c`
To find out `c`, insert values of the `m, x and y` coordinates from the given point.
`-5/24=(1/3)*(-7/15)+c`

`=>c=-5/24+1/3*7/15`

`=>c=-5/24+7/45`
`=>c=(-5*15+7*8)/360`
`=>c=(-75+56)/360`
`=>c=-19/360`

Answer 2

`y=1/3x-19/360`

Explanation:

The first answer is correct, but I would like to provide an alternative solution using the point-slope form.

Point-slope form:

Given a point `(x_0,y_0)` and a slope `m`, the equation of the line is:

`" "y-y_0=m(x-x_0)`

You just have to substitute everything.

Solution

`[1]" "y-y_0=m(x-x_0)`

`[2]" "y+5/24=1/3(x+7/15)`

`[3]" "y+5/24=1/3x+7/45`

`[4]" "y=1/3x+7/45-5/24`

`[5]" "y=1/3x+7/45-5/24`

`[6]" "y=1/3x+(56-75)/360`

`[7]" "color(blue)(y=1/3x-19/360)`