Question

What is the equation in point-slope form of the line passing through (–2, 1) and (4, 13)?

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 `(-2,1)` and `(4,13)`

Slope(`m`) = `(13-1)/(4-(-2))` = `12/6` = `2`

• Once the Slope is determined, pick any point on that line. Say `(-2,1)`, 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-1)=(2)*(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 `(4,13)`, and substitute it in our answer.

`(y-1) = 13-1 = 12`

`(2)*(x-(-2)) = (2)*(4-(-2)) = 2*6 = 12`

As the left hand side of the equation is equal to the right hand side, we can be sure that the point `(4,13)` does lie on the line.

• The graph of the line would look like this:
  graph{2x-y=-5 [-10, 10, -5, 5]}