Question

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

Answer 1

See a solution process below:

Explanation:

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]}