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

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]}