How do you find an equation of the line containing the given pair of points (0,0) and (5,7)?

1 Answer
Alan P.
Dec 27, 2016

#7x-5y=0#

Explanation:

For any two points on a straight line the ratio of the difference between the #y# values and the difference between the #x# values will be a constant. This constant is called the slope of the line.

For the given points #(0,0)# and #(5,7)# this slope will be
#color(white)("XXX")m=(Deltay)/(Deltax)=(7-0)/(5-0)=7/5#

For any arbitrary point on the line #(x,y)# and the point #(0,0)# on the line this slope must be the same value:
#color(white)("XXX")(y-0)/(x-0)=7/5#
or
#color(white)("XXX")y/x=7/5#
or
#color(white)("XXX")5y=7x#

There are various other forms in which this could be written; for example, "standard form" would be:
#color(white)("XXX")7x-5y=0#

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