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What is the equation of the line through points (2, 5) and (5, 7)?

1 Answer

Jul 28, 2016

#color(green)(2x-3y=-11)#

Explanation:

A line passing through #(2,5)# and #(5,7)# has a slope of
#color(white)("XXX")m=(Deltay)/(Deltax)=(7-5)/(5-2)=2/3#

Using the point #(2,5)# and this slope, the slope-point form for this line's equation is
#color(white)("XXX")y-5=2/3(x-2)#

This can be rearranged as
#color(white)("XXX")3y-15=2x-4#
or (in standard form)
#color(white)("XXX")2x-3y=-11#

Here's the graph that helps verify this result:
enter image source here

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