How do you write an equation in point-slope form for the given (–2, 1) and (4, 13)?

1 Answer
George C.
Aug 2, 2015

Use the slope formula to find slope #m = 2#, then use the second point to get:

#y - 13 = 2(x - 4)#

Explanation:

Given two points #(x_1, y_1)# and #(x_2, y_2)#, then the slope #m# of a line through those two points is given by the formula:

#m = (Delta y)/(Delta x) = (y_2 - y_1) / (x_2 - x_1)#

In our case, let #(x_1, y_1) = (-2, 1)# and #(x_2, y_2) = (4, 13)#. Then:

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

Then point slope form for a line is:

#y - y_0 = m(x - x_0)# where #m# is the slope and #(x_0, y_0)# is some point on the line. To avoid double minus signs, let's use the second point #(4, 13)# to get:

#y - 13 = 2(x-4)#

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