Question

What is the equation of the line passing through `(8,4)` and `(0,-2)`?

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)(-2) - color(blue)(4))/(color(red)(0) - color(blue)(8)) = (-6)/-8 = 3/4`

We know from the point `(0, -2)` the `y`-intercept is `-2`. The `y`-intercept is the point where `x = 0` and the line crosses the `y`-axis.

We can use the slope-intercept formula to write and equation for the line. 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.

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

`y = color(red)(3/4)x + color(blue)((-2))`

`y = color(red)(3/4)x - color(blue)(2)`