Question

How do you write an equation written in point slope form passing through the points (−6, 4) and (2, 0)?

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 `(-6,4)` and `(2,0)`

Slope(`m`) = `(0-4)/(2-(-6))` = `(-4)/8` = `-1/2`

• Once the Slope is determined, pick any point on that line. Say `(2,0)`, 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-0)=(-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 `(-6,4)`, and substitute it in our answer.

`(y-0) = 4-0 = 4`

`(2)*(x-2) = (-1/2)*(-6-2) = (-1/2)*(-8) = 4`

As the left hand side of the equation is equal to the right hand side, we can be sure that the point `(-6,4)` does lie on the line.

• The graph of the line would look like this:
  graph{y=-.5x+1 [-12.66, 12.65, -6.33, 6.33]}