Question

How do you determine the intercepts of `y=5x-13`?

Answer 1

The y-intercept is: -13 or (0, -13).

The x-intercept is 13/5 or (13/5, 0)

Explanation:

Because this equation is in the slope-intercept form `y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and and `color(blue)(b)` is the y-intercept we know for this equation the y-intercept is: -13 or (0, 13).

To find the `x` intercept we need to set `y = 0` and solve for `x`:

`0 = 5x - 13`

`0 + color(red)(13) = 5x - 13 + color(red)(13)`

`13 = 5x - 0`

`13 = 5x`

`13/color(blue)(5) = (5x)/color(blue)(5)`

`13/5 = (color(blue)(cancel(color(black)(5)))x)/cancel(color(blue)(5))`

`13/5 = x` or `x = 13/5`

Therefore the x-intercept is 13/5 or (13/5, 0)