Question

A line passes through point (2, 5) and has a slope of 3. Write an equation in Ax +By=C form for this line. Use integers for A, B, and C. ​

Answer 1

`3\, x + (-1)\, y = 1`.

Explanation:

Both the slope of this line and the coordinates of a point on this line are given. Therefore, start by finding the point-slope equation of this line: if the slope of a line in a plane is
`m`, and this line goes through a point at
`(x_(0),\, y_(0))`, the point-slope equation of this line will be
`(y - y_(0)) = m\, (x - x_(0))`.

The slope of the line in this question is
`m = 3`. It is given that this line goes through the point
`(2,\, 5)`, where
`x_(0) = 2` and
`y_(0) = 5`. Substitute in these values to find the point-slope equation of this line:

`(y - y_(0)) = m\, (x - x_(0))`.

`(y - 5) = 3\, (x - 2)`.

Rewrite this point-slope equation in the requested format:

`y - 5 = 3\, x - 6`.

`3\, x - 6 = y - 5`.

`3\, x = y + 1`.

`3\, x - y = 1`.

`3\, x + (-1)\, y = 1`.