Question

What is the equation of the line between `(3,16)` and `(2,4)`?

Answer 1

In slope-point form: `(y-4)=12(x-2)`

In standard form: `12x-y=20`

Explanation:

The slope between the points `(3,16)` and `(2,4)` is
`color(white)("XXX")m=(Delta y)/(Delta x)= (16-4)/(3-2) = 12`

The general slope-point form for a line with slope `m` through a point `(barx,bary)` is
`color(white)("XXX")(y-bary)=m(x-barx)`

Using the slope determined above and the point `(2,4)` (either point could have been used and would generate equivalent results)
`color(white)("XXX")(y-4)=12(x-2)`

Conversion to standard form
`color(white)("XXX")Ax+By=C`
only requires simple common operations.