How do you calculate the slope, x intercept, and y intercept of the following equation: #3x+6y = 9#?

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Answer 1 · 2015-07-31T22:31:50

The slope is #-1/2#.
The y-intercept is #3/2#.
The x-intercept is #3#.

Get the equation into slope-intercept form #y=mx+b# by solving for #y#. In the equation #y=mx+b#, #m# is the slope, and #b# is the y-intercept.

#6y=-3x+9#

Divide both sides by #6#.

#y=-3/6x+9/6# =

#y=-1/2x+3/2#

The slope is #-1/2# and the y-intercept is #3/2#.

To find the x-intercept, set #y# to zero, and solve for #x#.

#0=-1/2x+3/2#

Subtract #3/2# from both sides.

#-3/2=-1/2x#

Multiply both sides times #2#.

#-3=-x#

Multiply both sides times #-1#.

#3=x#

The x-intercept is #3#.

graph{3x+6y=9 [-10, 10, -5, 5]}