Question

How do you write the equation of a line that passes through (1,1) and has slope 1/4?

Answer 1

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

Answer 2

• The Point-Slope form of the Equation of a Straight Line is:

`(y-k)=m*(x-h)`
`m` is the Slope of the Line

`(h,k)` are the co-ordinates of any point on that Line.

• Here, we have been given the coordinates `(h,k)` of 1 point on that line as `(1,1)`
  And the Slope `m` is given as `1/4`

Substituting the values of h, k and m in the Point-Slope form, we get

`(y-1)=(1/4)*(x-1)`
The above will be the Equation of the Line in Point-Slope form.

• If we need it in the Slope Intercept Form, we need to follow these steps:

Multiplying both sides with 4, we get:

`4*(y-1)=x-1`

`4y-4=x-1`

`4y=x-1+4`

`4y=x+3`

We get the equation of the line as :
`y=(1/4)*x+3/4`

The graph will look like this:

graph{y=(1/4)*x+3/4 [-10, 10, -5, 5]}