How to find the slope and y-intercept for #y-2x<6#?

2 Answers
Meave60
Nov 20, 2017

#y<2x+6#

The slope is #2# and the y-intercept is #6#.

Explanation:

#y-2x<6#

Solve for #y# to get the inequality into slope-intercept form:

#y=mx+b#,

where:

#m# is the slope, and #b# is the y-intercept.

Solve for #y#.

#y-2x<6#

Add #2x# to both sides.

#y<2x+6#

The slope is #2# and the y-intercept is #6#.

Andy Y.
Nov 20, 2017

#y#-intercept: #(0, 6)#
Slope: #m=2#
The solution for #y# is given by the graph below.

Explanation:

The easiest way to evaluate this inequality is to pretend (for a moment) that we are actually dealing with the equation,

#y-2x = 6#

The #y# intercept of an equation occurs when #x=0#.

#y-2x = 6#

#y-2(0) = 6#

#y = 6#

So the #y#-intercept is the point #(0, 6)#. The #x#-intercept occurs when #y=0#.

#y - 2x = 6#

#0 - 2x = 6#

#-2x = 6#

#x = -3#

So the #x#-intercept is the point #(-3, 0)#. Draw a dashed line through these points to account for the inequality symbol.

The slope is the rise over the run.

#m="rise"/"run"=6/3=2#

Desmos.com and MS Paint

The final step is to determine where to shade by choosing an easy point, like #(0, 0)#. If plugging in this point makes the original inequality a true statement, then shade that entire side of the line.

#y-2x<6#

#0-2(0)<6#

#0 < 6# is true.

So shade the side with the point #(0, 0)#

Desmos.com and MS Paint

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