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

2 Answers
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(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]}