Question

Graph and shade the following inequality -5x+2y<-10

Answer 1

Answer: The graph is attached.

Explanation:

The equation of the line in Slope-intercept form is:

`y=mx+b`

Where m is the slope and b is the y-intercept.

You can solve for "y":

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

You need to rewrite the expression:

`y=(5)/(2)x-5`

You can identify that the slope of this line is:

`m=(5)/(2)`

And the y-intercept is:

`b=-5`

Substitute
`y=0` and solve for "x" to know the x-intercept:

`0=(5)/(2)x-5\\\\5*2=5x\\\\x=2`

Now you know that the line passes through the points (0,-5) and (2,0).

Since the inequality is "<", you know that the line must be dashed and the shaded region must be below the line
`y=(5)/(2)x-5`.

Knowing this, you can graph it (Observe the graph attached)