How do you graph #5x + y < 7#?

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Answer 1 · 2018-03-24T10:34:33

See a solution process below:

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For: #x = 0#

#(5 * 0) + y = 7#

#0 + y = 7#

#y = 7# or #(0, 7)#

For: #x = 1#

#(5 * 1) + y = 7#

#5 + y = 14#

#-color(red)(5) + 5 + y = -color(red)(5) + 7#

#0 + y = 2#

#y = 2# or #(1, 2)#

We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

graph{(x^2+(y-7)^2-0.125)((x-1)^2+(y-2)^2-0.125)(5x+y-7)=0 [-20, 20, -10, 10]}

Now, we can shade the left side of the line.

The boundary line will be changed to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(5x+y-7)<0 [-20, 20, -10, 10]}