Question

How do you write an equation in point-slope form for the line passing through the points (2,8) and (3,4)?

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.

• To find the Equation of the Line in Point-Slope form, we first need to Determine it's Slope . Finding the Slope is easy if we are given the coordinates of two points.

Slope(`m`) = `(y_2-y_1)/(x_2-x_1)` where `(x_1,y_1)` and `(x_2,y_2)` are the coordinates of any two points on the Line

The coordinates given are `(3,4)` and `(2,8)`

Slope(`m`) = `(8-4)/(2-3)` = `4/-1` = `-4`

• Once the Slope is determined, pick any point on that line. Say `(2,8)`, and Substitute it's co-ordinates in `(h,k)` of the Point-Slope Form.

We get the Point-Slope form of the equation of this line as:
`(y-8)=(-4)*(x-2)`

• Once we arrive at the Point-Slope form of the Equation, it would be a good idea to Verify our answer. We take the other point `(3,4)`, and substitute it in our answer.

`(y-8) = 4-8 = -4`

`(-4)*(3-2) = (-4)*1 = -4`

As the left hand side of the equation is equal to the right hand side, we can be sure that the point `(3,4)` does lie on the line.

• The graph of the equation would look like this:

graph{-4x+16 [-18.51, 18.55, -9.27, 9.26]}