How do you graph #x+5y<=10# on the coordinate plane?

Question

3061 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-19T21:12:25

See a solution process below:

First, change the inequality to a quality and find two points that are solutions to the equality:

For #x = 0#:

#0 + 5y = 10#

#5y = 10#

#(5y)/color(red)(5) = 10/color(red)(5)#

#(color(red)(cancel(color(black)(5)))y)/cancel(color(red)(5)) = 2#

#y = 2# or #(0, 2)#

For #y = 0#

#x + (5 * 0) = 10#

#x + 0 = 10#

#x = 10# or #(10, 0)#

We can now plot the two points on the grid and draw a line through the points to draw the boundary of the inequality:

graph{(x^2+(y-2)^2-0.025)((x-10)^2+y^2-0.025)(x+5y-10)=0 [-12, 12, -6, 6]}

Because it is an inequality and the operator is "less than or equal to" the line will remain solid for graphing the inequality.

And, because it is a "less than" inequality we will shade to the left of the line.

graph{(x+5y-10)<=0 [-12, 12, -6, 6]}