Question

How do you write an equation of a line through: (2,4) and (5,1)?

Answer 1

`y - 4 = -1(x - 2)` or `y = -x + 6`

Explanation:

To write this equation we can use the point-slope formula. To use this formula we must first 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.

Using the two points given in the problem the slope is:

`m = (1 - 4)/(5 - 2)`

`m = -3/3`

`m = -1`

Now we can use the point-slope formula to determine the equation:

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.

Using the slope we calculate and one of the points gives:

`y - 4 = -1(x - 2)`

Solving for `y` to put this equation into the slope-intercept form gives:

`y - 4 = -x + 2`

`y - 4 + 4 = -x + 2 + 4`

`y - 0 = -x + 6`

`y = -x + 6`