Question

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

Answer 1

`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`