Question

How do you write the equation for a line that passes through points (2,1) and (0,7)?

Answer 1

`y - 7 = -3x` or `y = -3x + 7`

Explanation:

To find the equation of a line passing through two points you must first find the slope of the line.

The slope can be found by using the formula: `color(red)(m = (y_2 = y_1)/(x_2 - x_1)`
Where `m` is the slope and `(x_1, y_1)` and `(x_2, y_2)` are the two points. Substituting the two points give in the problem allows us to calculate the slope as:

`m = (7 - 1)/(0 - 2)`

`m = 6/(-2)`

`m = -3`

Next we can use the point-slope formula to find the equation for the line passing through these two points.

The point-slope formula states: `(y - y_1) = m(x - x_1)`
Where `m` is the slope and #(x_1, y_1) is a point the line passes through.

We can substitute `-3` for me and (0, 7) for the point giving:

`y - 7 = -3(x - 0)`

`y - 7 = -3x - 3*0`

`y - 7 = -3x`

Solving for the slope intercept form gives:

`y - 7 + 7 = -3x + 7`

`y - 0 = -3x + 7`

`y = -3x + 7`