How do you graph the equation #y<=2x+3#?

1 Answer
smendyka
Aug 9, 2017

First, find two points which solve the this if it is written as an equation and plot these two points on the grid then draw a line through the two points:

For #x = 0#:

#y = (2 * 0) + 3#

#y = 0 + 3#

#y = 3# or #(0, 3)#

For #x = 2#:

#y = (2 * 2) + 3#

#y = 4 + 3#

#y = 7# or #(2, 7)#

graph{(y - 2x - 3)(x^2 + (y-3)^2 - 0.125)((x - 2)^2 + (y - 7)^2 - 0.125) = 0 [-20, 20, -10, 10]}

Because the inequality is "less than or equal to" we can draw a solid line through the two points. And, also because it is "less than or equal to" we need to shade below the line.

graph{(y - 2x - 3) <= 0 [-20, 20, -10, 10]}

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