How do you write in point slope form an equation of the line through each pair of points (2,7) and (-4,1)?

1 Answer
KillerBunny
Apr 5, 2015

Two points uniquely identify a line, and the formula we must use is the following: when given two points #(x_1,y_1)# and #(x_2,y_2)#, the line passing through both of them is

#frac{y-y_2}{y_1-y_2}=\frac{x-x_2}{x_1-x_2}#

Plugging the values #(x_1,y_1)=(2,7)# and #(x_2,y_2)=(-4,1)# into that formula, we get

#\frac{y-1}{7-1}=\frac{x+4}{2+4} \iff \frac{y-1}{6} = \frac{x+4}{6} \iff y-1 = (x+4)#

Which can be brought into the standard form:

#y-1 = x+4 \iff y = x+5#

You can easily check that this is the right solution, because for both points #(2,7)# and #(-4,1)# you have that the #y# coordinate equals the #x# one plus #5#.

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