Question

How do you find an equation of the line with slope 3 that contains the point (4, 1)?

Answer 1

• 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 `(4,1)`
  And the Slope `m` is given as `3`

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

`(y-1)=3*(x-4)`
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:

`(y-1)=3x - 12`

`y=3x - 12 + 1`

`y=3x - 11`

We get the equation of the line as :

`color(green)( y=3x - 11`

The graph will look like this:

graph{ y=3x - 11 [-10, 10, -5, 5]}