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

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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 $x = 0$ $x = 0$ :

$0 + 5 y = 10$ $0 + 5y = 10$

$5 y = 10$ $5y = 10$

$\frac{5 y}{5} = \frac{10}{5}$ $(5y)/color(red)(5) = 10/color(red)(5)$

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

$y = 2$ 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]}

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