How do you write the equation of a line in point slope form and slope intercept form given points (2, 7) (1, -4)?

1 Answer
May 23, 2015

The slope of the line segment between two points is the change in #y# divide by the change in #x#.

For the case of a line through #(2,7)# and #(1,-4)# we have

slope #m = (Delta y)/(Delta x) = (-4-7)/(1-2) = -11/-1 = 11#

Using the point #(2,7)# we can write the equation of the line in point slope form as:

#y-7 = m(x - 2)# where the slope #m = 11#.

That is:

#y - 7 = 11(x - 2)#

To get point intercept form, first expand the right hand side so...

#y - 7 = 11x - (11*2) = 11x - 22#

Then add #7# to both sides to get:

#y = 11x - 15 = 11x + (-15)#

This is point intercept ( #y = mx+c# ) form with slope #m = 11# and intercept #c = -15#.