Question

How do you find the equation, x-intercept, and the y-intercept for the line with an y-intercept of 5 and a slope of -1/3?

Answer 1

See the entire solution process below:

Explanation:

We can use the slope intercept formula to write the equation of 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 information from the problem gives:

`y = color(red)(-1/3)x + color(blue)(5)`

The y-intercept was given as part of the problem: `color(blue)(b = 5)` or `(0, 5)`

To find the x-intercept we set `y` equal to `0` and solve for `x`:

`y = color(red)(-1/3)x + color(blue)(5)` becomes:

`0 = color(red)(-1/3)x + color(blue)(5)`

`0 - 5 = color(red)(-1/3)x + color(blue)(5) - 5`

`-5 = color(red)(-1/3)x + 0`

`-5 = color(red)(-1/3)x`

`-3 xx -5 = -3 xx color(red)(-1/3)x`

`15 = color(red)(cancel(color(blakc)(-3))) xx cancel(color(red)(-1/3))x`

`15 = x`

The x-intercept is `15` or `(15, 0)`