How do you write the equation of a line in slope intercept, point slope and standard form given (3,5) and (1,2)?

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Answer 1 · 2017-07-02T21:13:18

# y = 3/2 x+1/2 #

There are generally two techniques for finding the equation of a straight line that passes through the points #(x_1,y_1)# and #(x_2,y_2)#.

The first technique is to use the point-point equation:

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

The second technique is to use the point-slope equation:

# y-y_1 = m(x-x_1)# where the slope #m# is calculated using:
# m = (Delta y)/(Delta x) = (y_2-y_1)/(x_2-x_1) #

So for the given coordinates #(3,5)# and #(1,2)#.

Using the first method the equation would be:

# (y-5)/(2-5) = (x-3)/(1-3) #
# :. (y-5)/(-3) = (x-3)/(-2) #
# :. y-5 = 3/2 x-9/2 #
# :. y = 3/2 x+1/2 #

Using the second method the slope would be:

# m = (2-5)/(1-3) = (-3)/(-2) = 3/2#

So the equation would be :

# y-5=3/2(x-3) #
# :. y-5=3/2x-9/2 #
# :. y = 3/2 x+1/2 #, as before