Question

How do you write an equation of the line that passes through the given points (0,0), (4,-20)?

Answer 1

`(y + color(red)(20)) = color(blue)(-5)(x - color(red)(4))`

Or

`y = -5x`

Explanation:

The point-slope formula can be used to write an equation for this line. First, we must determine the slope. The slope can be found by using the formula: `m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

Where `m` is the slope and (`color(blue)(x_1, y_1)`) and (`color(red)(x_2, y_2)`) are the two points on the line.

Substituting the values from the two points in the problem gives:

`m = (color(red)(-20) - color(blue)(0))/(color(red)(4) - color(blue)(0))`

`m = (-20)/4 = -5`

The point-slope formula states: `(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))`

Where `color(blue)(m)` is the slope and `color(red)(((x_1, y_1)))` is a point the line passes through.

Substituting the slope we calculated and the second point gives:

`(y - color(red)(-20)) = color(blue)(-5)(x - color(red)(4))`

`(y + color(red)(20)) = color(blue)(-5)(x - color(red)(4))`

We can also substitute the slope we calculated and the first point giving:

`(y - color(red)(0)) = color(blue)(-5)(x - color(red)(0))`

`y = -5x`