Question

How do you find the equation of the line that passes through the points (7,3) and (2,5)?

Answer 1

`y - 3 = -2/5(x - 7)` or `y = -2/5x + 29/5`

Explanation:

To find the line passing through these two points we will use the point-slope formula. However, first we must determine the slope.

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.

For our problem we can substitute and find the slope as:

`m = (5 - 3)/(2 - 7)`

`m = 2/(-5) = -2/5`

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

Substituting the slope we calculated and one of the points we were given.

`y - 3 = -2/5(x - 7)`

or, converting to slope-intercept form:

`y - 3 = -2/5x + 14/5`

`y - 3 + 3 = -2/5x + 14/5 + 3`

`y - 0 = -2/5x + 14/5 + 3(5/5)`

`y = -2/5x + 14/5 + 15/5`

`y = -2/5x + 29/5`