Question

Graph the linear inequality 5x + 2y <10.

Answer 1

Here are the steps in graphing the linear inequality.

1. Convert the linear inequality into a slope-intercept form or by converting the equation into y = or y > or y <.

a. Isolate the variable "y" on the left side of the inequality by subtracting 5x on both sides of the inequality.

`5x-5x+2y<10-5x`
`2y<10-5x`

b. Divide both sides of the inequality by 2.

`(2y)/(2)<(10)/(2)-(5x)/(2)`
`y<5-(5)/(2)x`

c. Rearrange the terms on the right side.

`y<-(5)/(2)x+5`

2. From the converted inequality, we can see that the slope is -5/2 while the y-intercept is 5.

Let's plot the y-intercept at (0, 5) first.

Then, using the slope -5/2, let's find another point that is 5 units downward and 2 units to the right of the y-intercept.

3. Connect the dots using a dotted line since the inequality symbol is <. Then, shade the part below the line since the inequality symbol is "less than".

The final graph of the given linear inequality is shown below: