graph the region described by -4x+5y<20

Question

graph the region -4x+5y<20

Answer 1

-4x + 5y < 20

 

Add 4x to both sides of the inequality:

 

5y < 4x + 20

 

Divide both sides by +5:

 

y < (4/5)x + 4

 

Graph a dashed line y = (4/5)x + 4.

Dashed to indicate the points on the line are not part of the solution set.

 

Now shade everything below the line; that's the solution set.

 

Here's a GeoGebra graph:

http://www.wyzant.com/resources/files/264526/2d_inequality_graph

Answer 2

Hi Maggie;

The line will be dotted because < does NOT include the = sign...

-4x+5y<20

The equation is almost in Standard Form...

Standard Form is...

Ax+By=C, A>0

While it is true that the original equation does NOT have an = sign, it is also true that the equation for the dotted line will have an = sign.

-4x+5y<20

A is less than zero.

Let's multiply both sides by -1.  Because this is a negative number, the < will change to >...

4x-5y>20

Equation for dotted line...

4x-5y=10

Slope of a standard equation is...

-A/B...

-4/-5

4/5.

Let's establish the y-intercept.  This is the value of y when x=0.  This is also known as C/B...

y=10/-5=-2

The y-intercept is (0,-2)...

Let's also establish the x-intercept.  This is the value of x when y=0.  This is also known as C/A...

x=10/4=5/2

(5/2,0)

We now have two points, and the slope.

Plot each point, and draw the line.  Because the slope is 4/5, as the line rises 4 units, it should move 5 units to the right.  As the line descends 4 units, it should move 5 units to the left.

Slope-intercept form of this dotted line would be...

y=mx+b, m is slope, b is y-intercept.

-4x+5y<20

5y<4x+20

y<(4/5)x+4

Shade the region beneath the dotted line.