Question

What is the equation below that represents the line that passes through the point (2, 4) and has a a slope of 3?

Answer 1

`y - 4 = 3(x - 2)` or in standard form `y = 3x - 2`

Explanation:

The point-slope formula gives the equation of a line given the slope and a point. This formula is:

`color(red)((y - y_1) = m(x - x_1))`

where `m` is the slope and #(x_1, y_1) is the point.

Substituting the information provided into the point-slope formula gives:

`y - 4 = 3(x - 2)`

Putting into standard form gives:

`y - 4 = 3x - 6`

`y - 4 + 4 = 3x -6 + 4`

`y - 0 = 3x - 2`

`y = 3x - 2`