How do you graph #x-4y=-8#?

Question

How do you graph #x-4y>=-8#?

Eli Assouline · Accepted Answer

See the explanation

#color(brown)("Making the "y" term positive")#

Multiply by (-1)

#-x+4y<=-8" "larr" notice that the ">=" is now "<=#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("Isolate the "y" term")#

Add #x# to both sides

#-x+x+4y<=-8+x#

#4y<=x-8#
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#color(brown)("Isolate the "y)#

Divide both sides by 4

#4/4xx y<=x/4-8/4#

#y<=x/4-2#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("Now plot your graph the normal way")#

At #y=0 -> x=8#
At #x=0-> y=-2#

Avery Alexander · Answer

undefined To graph the inequality $ x - 4y \geq -8 $, follow these steps:

1. Start by graphing the boundary line $ x - 4y = -8 $ as if it were an equation (i.e., replace the inequality symbol with an equal sign).
2. To graph the line, rearrange the equation to slope-intercept form $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept.
3. For the given equation, rearrange it to $ y = \frac{1}{4}x + 2 $.
4. Plot the y-intercept at (0, 2), then use the slope of $ \frac{1}{4} $ to find another point on the line (move 1 unit to the right and 4 units up).
5. Draw a solid line through these two points to represent the boundary of the inequality.

Since the inequality is $ x - 4y \geq -8 $, shade the region above the boundary line because it includes all points where $ x - 4y $ is greater than or equal to -8.

How do you graph #x-4y&gt;=-8#?

How do you graph #x-4y>=-8#?