Question

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

Answer 1

`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: