Question

How do you find the slope of a line parallel to `Y-3=0`?

Answer 1

See a solution process below:

Explanation:

We can rewrite this equation as:

`y - 3 + color(red)(3) = 0 + color(red)(3)`

`y - 0 = 3`

`y = 3`

This equation represents a horizontal line where for each and every value of `x`, `y` is equal to `3`.

By definition, the slope of a horizontal line is `0`.

We can also show this by writing this equation in slope-intercept form. 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.

`y = color(red)(0)x + color(blue)(3)`

Therefore, the slope is: `color(red)(m = 0)`