Question

How do you write the equation of the line between the points (2, 4) and (-2,8)?

Answer 1

See full process description below:

Explanation:

We can use the point-slope formula to write this equation.

However, first we must find 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 two points from the problem gives:

`m = (color(red)(8) - color(blue)(4))/(color(red)(-2) - color(blue)(2))`

`m = 4/-4`

`m = -1`

Now we can use the point slope formula.

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 calculate and one of the points gives:

`(y - color(red)(4)) = color(blue)(-1)(x - color(red)(2))`

Putting this in the more familiar slope-intercept form by solving for `y` gives:

`y - color(red)(4) = color(blue)(-1)x - (color(blue)(-1) xx color(red)(2))`

`y - color(red)(4) = color(blue)(-1)x - (-2)`

`y - color(red)(4) = color(blue)(-1)x + 2`

`y - color(red)(4) + 4 = color(blue)(-1)x + 2 + 4`

`y - 0 = color(blue)(-1)x + 6`

`y = -x + 6`

Answer 2

`x+y-6=0`

Explanation:

You can find the line by the following formula:

`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`

where `(x_1;y_1)` and `(x_2;y_2)` are the given points.

Then the line is:

`(y-4)/(8-4)=(x-2)/(-2-2)`

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

`y-4=-x+2`

`x+y-6=0`