Question

How do you write the slope-intercept form of the line with (-5,0) and (8,-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)(0))/(color(red)(8) - color(blue)(-5)) = (color(red)(-4) - color(blue)(0))/(color(red)(8) + color(blue)(5)) = -4/13`

The slope-intercept form of a linear equation is: `y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept value.

We can solve for `color(blue)(b)` by substituting the slope we just calculated and one of the points in the problem for `x` and `y`:

`0 = (color(red)(-4/13) * -5) + color(blue)(b)`

`0 = 20/13 + color(blue)(b)`

`0 - 20/13 = 20/13 - 20/13 + color(blue)(b)`

`-20/13 = 0 + color(blue)(b)`

#-20/13 = color(blue)(b)

We can substitute the slope we calculated and the value of `color(red)(b)` we calculated into the formula to write the equation of the line.

`y = color(red)(-4/13)x + color(blue)(-20/13)`

`y = color(red)(-4/13)x - color(blue)(20/13)`