Graphing Inequalities

Question

-x+0.25y (is greater than or equal to) -1.75

 

What are the coordinates with which I would graph this?

 

Answer 1

Hi Sara, start by finding the x- and y-intercept points. You can do this by changing the greater than or equal sign to an equal sign and solve for x and y.

 

This gives:

 

-x + 0.25y = -1.75

 

Set x = 0, solve for y:

 

0.25y = -1.75

 

Divide both sides by 0.25:

 

y = -7

 

The y-intercept point is: (0, -7)

 

Set y = 0, solve for x:

 

-x = -1.75

 

Multiply both sides by -1:

 

x = 1.75

 

The x-intercept point is: (1.75, 0)

 

With these two points you can plot the line. Since you have greater than or equal to, the line will be solid.

 

Next, pick a point on the graph to see what side of the line to shade. Pick the point: (0, 0) and substitute for the x- and y-values in the inequality.

 

-x + 0.25y ≥ -1.75

 

0 + 0 ≥ -1.75, this is true, therefore, shade the side of the line where the point, (0, 0) lies.

 

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