Question

How do you find the equation of the line that goes through `(- 4,3)` and `( 5,- 2)`?

Answer 1

See a solution process below:

Explanation:

First, we need to determine the slope of the line. The formula for find the slope of a line is:

`m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

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

Substituting the values from the points in the problem gives:

`m = (color(red)(-2) - color(blue)(3))/(color(red)(5) - color(blue)(-4)) = (color(red)(-2) - color(blue)(3))/(color(red)(5) + color(blue)(4)) = -5/9`

Now, we can 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 above and the values from the first point in the problem gives:

`(y - color(blue)(3)) = color(red)(-5/9)(x - color(blue)(-4))`

`(y - color(blue)(3)) = color(red)(-5/9)(x + color(blue)(4))`

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

`(y - color(blue)(-2)) = color(red)(-5/9)(x - color(blue)(5))`

`(y + color(blue)(2)) = color(red)(-5/9)(x - color(blue)(5))`