Question

What is the equation of a line that has a slope of 2 and passes through the point (4,6) ?

Answer 1

`y-6=2\,(x-4)`

or in slope y-intercept form :

`y=2x-2`

Explanation:

The easiest way of find the answer for this is to use what is called the "point-slope" form of a line, because you are in fact given the value of the slope (m) and also a point
`(x_0,y_0)` it goes through:

`y-y_0=m\,(x-x_0)`

In our case the equation becomes:

`y-y_0=m\,(x-x_0)\\y-6=2\,(x-4)\\`

This can also be written in the slope-intercept form by solving for "y" and operating to remove the parenthesis:

`y-6=2\,(x-4)\\y=2x-8+6\\y=2x-2`