Question

How do you find the equation, x-intercept, and the y-intercept for the line that passes through (-3,1) with a slope of zero?

Answer 1

See a solution process below:

Explanation:

A line with slope `0` by definition is a horizontal line.

Horizontal lines have the same value for `y` for each and every value of `x`.

Because the `y` value of the point given in the problem is `1` then the equation is:

`y = 1`

y-intercept

Because the value of the equation is the same for each and every value of `x`, when we set `x` equal to `0` to find the `y` intercept, `y = 1`

Therefore, the `y`-intercept is: `1` or `(0, 1)`

x-intercept

Because this is a horizontal line it is by definition parallel to the `x` axis. Because it is parallel to the `x` axis it never crosses the `x` axis.

Therefore the is no `x`-intercept.