Question

How do you write an equation of a line given (5, -2); (-16, 4)?

Answer 1

See a solution process below:

Explanation:

First, we need to determine the slope of the line. 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 points in the problem gives:

`m = (color(red)(4) - color(blue)(-2))/(color(red)(-16) - color(blue)(5)) = (color(red)(4) + color(blue)(2))/(color(red)(-16) - color(blue)(5)) = 6/-21 = -2/7`

We can now use the point-slope formula to write an equation for the line. The point-slope form of a linear equation is: `(y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))`

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

Substituting the slope we calculated and the values from the first point in the problem gives:

`(y - color(blue)(-2)) = color(red)(-2/7)(x - color(blue)(5))`

`(y + color(blue)(2)) = color(red)(-2/7)(x - color(blue)(5))`

We can also substitute the slope we calculated and the values from the second point in the problem giving:

`(y - color(blue)(4)) = color(red)(-2/7)(x - color(blue)(-16))`

`(y - color(blue)(4)) = color(red)(-2/7)(x + color(blue)(16))`