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

Jun 1, 2018

$y = - 5$

#### 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.

Jun 1, 2018

Point-slope form: $y + 5 = 0 \left(x + 3\right)$

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 $\left(- 3 , - 5\right)$.

Point-slope form: $y - {y}_{1} = m \left(x - {x}_{1}\right)$,

where:

$m$ is the slope, and $\left({x}_{1} , {y}_{1}\right)$ is the point.

$m = 0$

${y}_{1} = - 5$

${x}_{1} = - 3$

Plug in the known values.

$y - \left(- 5\right) = 0 \left(x - \left(- 3\right)\right)$

$y + 5 = 0 \left(x + 3\right)$ $\leftarrow$ point-slope form

Slope-intercept form: $y = m x + b$,

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 $y$.

$y + 5 = 0$

$y = - 5$ $\leftarrow$ slope-intercept form

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