How do you write an equation of a line with point (5,-2), (7,1)?

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Answer 1 · 2018-05-26T06:14:52

#y=3/2x-19/2#

Find slope first: #(y_2-y_1)/(x_2-x_1)#
Let's have point 1 as (#5,-2#) and point 2 as (#7,1#)

points are #(x,y)# format, so in #(5,-2)#, #x_1 = 5# and #y_1=-2# and in #(7,1)#, #x_2=7# and #y_2=1#

Therefore the solution will be like this:

Thus, slope #m# is: #(1-(-2))/(7-5)#
Simplifying, #(1+2)/(7-5)=3/2#

Let's use point-slope formula, #y-y_1=m(x-x_1)#
Adding in values, #y-(-2)=3/2(x-5)#

Now simplify and you get your equation. Make sure to isolate #y#

#y+2=3/2x-15/2#
#y=3/2x-15/2-2\rArr3/2x-15/2-2#
#\rArry=3/2x-19/2#