how do I find he points of an equation

Question

What are the points for the following equations?

 

 

1.   3x + y < 5

 

 

2.        x < 2y

     x + y < 0

 

 

 

Answer 1

3X + y < 5

 

  Y < -3X +5 

 

  Graph line Y = -3X +5 , with shaded , because it doesn't have = , to include points on the line.

   

   Y intercept : ( 0,5 )

 

    X intercept : ( 5/3 , 0)

   

    Test a point ( 0,0 )

 

     0 < -3(0) +5, we see that it satisfies the condition of inequality.

     

      Shade all the area to the left of the line from the intercept points as a solution.

  

Answer 2

Your problems are to find the solution sets to inequalities and systems of inequalities.

 

1. Find solutions to the inequality:

 

3x + y < 5

 

y < -3x + 5

 

Graph y = -3x + 5 with a dashed line to signify that the points on the line are NOT part of the solution set to the inequality.

 

Shade the entire region of the coordinate plane BELOW the line; all points in the shaded region are in the solution set to the inequality.

2. Find the solution set to the SYSTEM of inequalities:

x < 2y
x + y < 0

 

Solve for y in each:

 

y > 1/2 x

y < –x

 

Graph the lines y = 1/2 x and y = –x with dashed lines because the solution set does not include points on the lines.

 

Pick two colors or two patterns; use the first to shade above the line y = 1/2 x and use the second to shade below y = –x. The overlap of the two shadings contains the set of points that are solutions to the system of inequalities.

Answer 3

Hi L;

1. 3x + y < 5
I believe the points you are looking for are the x- and y-intercepts...

This equation will be graphed with a dotted line.  A complete line will NOT be used because the < does NOT include the = sign.  The < indicates which area should be shaded.

3x+y=5 is the equation of the dotted line.

The y-intercept is the value of y when x=0.

y=5, (0,5)

The x-intercept is the value of x when y=0

3x=5

x=5/3, (5/3,0)

2. x < 2y

This is also a dotted line.

Such line will be established with the equation of...

x=2y

The y-intercept is...

0=2y

0=y

(0,0)

The x-intercept is..

x=(2)(0)

x=0

(0,0)

x + y < 0

This is also a dotted line.

Such line will be established with the equation of...

x+y=0

y-intercept...

y=0, (0,0)

x-intercept...

x=0, (0,0)