Free Algebra
Tutorials!

Try the Free Math Solver or Scroll down to Tutorials!

Enter expression, e.g. (x^2-y^2)/(x-y)

Enter expression, e.g. x^2+5x+6

Enter expression, e.g. (x+1)^3

Enter a set of expressions, e.g. ab^2,a^2b

Enter equation to solve, e.g. 2x+3=4

Enter equation to graph, e.g. y=3x^2-1

Depdendent Variable

Number of equations to solve:

Equ. #1:

Equ. #2:

Equ. #3:

Equ. #4:

Equ. #5:

Equ. #6:

Equ. #7:

Equ. #8:

Equ. #9:

Solve for:

Enter inequality to solve, e.g. 2x+3>4

Enter inequality to graph, e.g. y<3x^2-1

Dependent Variable

Number of inequalities to solve:

Ineq. #1:

Ineq. #2:

Ineq. #3:

Ineq. #4:

Ineq. #5:

Ineq. #6:

Ineq. #7:

Ineq. #8:

Ineq. #9:

Solve for:

Math solver on your site

Please use this form if you would like
to have this math solver on your website,
free of charge.

Name:

Email:

Your Website:

Msg:

Graphing Technology: Parent and Family Graphs

Objective Use a graphing calculator to explore how changing the values of m and b affect the graph of y = mx + b .

In this lesson, you will be asked to explore the graphs of linear equations, and how they depend on the slope and the y-intercept. There are several main ideas that this lesson reinforces.

Key Ideas

• Lines with positive slope have the property that as we move to the right along the line, the line slopes upward.

• Lines with negative slope slope downward.

• Lines with zero slope are horizontal.

• Lines with greater positive slope move upward more steeply. Lines with lesser negative slope move downward more steeply.

Try to explore both positive and negative values of m by graphing equations of the form y = mx . The collection of lines obtained in this way can be thought of as a family of lines. A family of lines is shown below.

Any one of the lines in the family can be thought of as a parent, since the other members of the family are obtained by rotating that line. Typically a simple member, such as y = x , is the parent graph.

Key Idea

In graphing an equation of the form y = mx + b ,

• the line shifts up as the value of b increases, and

• the line shifts down as the value of b decreases.

Try to explore by graphing equations of the form y = x + b for various values of b, both positive and negative. The lines are simply a family of parallel lines that move up or down. Again, a simple member, such as y = x , is the parent graph. A family of graphs is shown below.

Next, try to explore the following different families of lines, y = 2x + b and y = -x + b , for various values of b. You will again find families of parallel lines, with slopes 2 and -1, respectively.

“What can you say about lines having the same slope?”

The answer to this question is that they are parallel.