Question

What is the slope-intercept form of the line passing through `(-2, -1)` and `(0, -6)`?

Answer 1

See the entire solution process below:

Explanation:

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.

First 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)(-6) - color(blue)(-1))/(color(red)(0) - color(blue)(-2)) = (color(red)(-6) + color(blue)(1))/(color(red)(0) + color(blue)(2)) = -5/2`

The point `(0, -6)` is the y-intercept (the value of `y` when `x` is `0`).

Substituting the slope we calculated and the y-intercept gives:

`y = color(red)(-5/2)x + color(blue)(-6)`

`y = color(red)(-5/2)x - color(blue)(6)`