Question

What is the equation of a horizontal line passing through (-3,-5)?

Answer 1

`y = -5`

Explanation:

If y always equals -5 then the x value will change but the y value will not. This means that the slope of the line is zero and will be parallel to the x axis, which is the horizontal line.

Answer 2

Point-slope form: `y+5=0(x+3)`

Slope-intercept form: `y=-5`

Explanation:

A horizontal line has a slope of `0`. We can use the point-slope form for a linear equation since we know the slope and the point `(-3,-5)`.

Point-slope form: `y-y_1=m(x-x_1)`,

where:

`m` is the slope, and `(x_1,y_1)` is the point.

`m=0`

`y_1=-5`

`x_1=-3`

Plug in the known values.

`y-(-5)=0(x-(-3))`

`y+5=0(x+3)` `larr` point-slope form

Slope-intercept form: `y=mx+b`,

where:

`m` is the slope and `b` is the y-intercept.

We can convert the point-slope form to slope-intercept form by solving for `y`.

`y+5=0`

`y=-5` `larr` slope-intercept form

graph{y+5=0(x+3) [-9.875, 10.125, -7.52, 2.48]}