Question

Write an equation that passes through the points (0,-5) and (8,-5)

Answer 1

Equation of the line:
`y = -5`.

Explanation:

Let
`(x_0,\, y_0)` and
`(x_1,\, y_1)` denote the coordinates of these two points, respectively.

Calculate the slope
`m` of this line:

`\displaystyle m = (y_1 - y_0)/(x_1 - x_0) = ((-5) - (-5))/(8 - 0) = 0`.

Notice that the slope is zero because the two points have the same
`y`-coordinates (
`y_0 = y_1 = -5`) even though their
`x`-coordinates are distinct (
`x_0 \\e x_1`.)

Equation for this line in point-slope form:

`y - y_0 = m\, (x - x_0)`.

`y - (-5) = 0\, (x - 0)`.

Rewrite and simplify to obtain the equation of this line in slope-intercept form:

`y = -5`.

The
`x`-term was eliminated because the slope was zero.