Solve and graph x -2y >8

Question

I need solve and graph 

Answer 1

Hello Ana,

 

Thank you for your post. In order to graph the inequality, you first need to solve it for y ( that means the variable y has to be alone on one side of the inequality)

 

Here is a similar example:

 

X - 3y > 15

-x          -x

 

First, you need to move x by subtracting it from both sides of the inequality. Keep in mind that 15 and x are different from one another and thus cannot be combined:

 

Now you have:

-3y>15-x

 

In order to get y alone, you need to divide by the number in front of y:

-3y/-3 > 15/-3 -x/-3

 

IMPORTANT: when you divide by a negative number, the DIRECTION of the inequality CHANGES!!

 

Y < -5 + 1/3x OR y < -5 + X/3

 

To graph this inequality: 

 

Start with the y-intercept (it is ALWAYS the number without a letter on the SAME SIDE as x, in this case it is -5). Put a point in the coordinate system on -5 on the y-axis. 

 

To get the full line, start at -5 and use the slope (ALWAYS THE NUMBER IN FRONT OF X DIRECTLY) to complete the line. The number in our case is 1/3 (NEVER include x). Again start at -5 and go up 1 (change in y, also called rise) step. Stop and now move to the right 3 steps (change in x, also called run).

 

Now you have 2 points that you can combine to create the line ( 0,-5) and (3, -4). 

IMPORTANT: your inequality does NOT contain an additional equal sign, therefore your line will be DOTTED)

 

In order to shade the correct area:

This inequality says < ( which means: LESS than). So you will need to shade the area BELOW (under) the line. 

 

I hope this helps. Please let me know if you need further help! 

 

-Stephanie

 

 

Answer 2

First, we solve for y in the inequality.

 

Subtract x on both sides of the inequality.

 

-2y > -x + 8

 

 

Divide both sides of the inequality by -2.

 

y > (1/2)x - 4

 

 

To graph, draw the line  y = (1/2)x - 4   on a coordinate system.

Shade the region on the coordinate system that is above this line.  That is your solution.