Intermath | Workshop Support

 Write-up

Title
Comparing lines.

Problem Statement

Let f(x) = ax + b, and g(x) = cx + d, where a, b, c, and d, are any real numbers.
If f(x) and g(x) are graphed, what can you conclude about a, b, c, and/or d, if:

a. f(x) and g(x) are parallel?
b. f(x) and g(x) are perpendicular?
c. f(x) does not cross the x-axis?
d. g(x) is vertical?
e. f(x) and g(x) have the same y-intercept?

Problem setup

Create a table, pick x values, find y, and graph. Review terms:  graph, table, coordinate, quadrants, line, equation, y-axis, x-axis, negative numbers, positive numbers, slope, real number, absolute value, parallel lines, perpendicular lines, vertical, y-intercept

Plans to Solve/Investigate the Problem

In Excel or on paper create a table with column headings:  x, y =2x + 1, y, (x,y).  Pick x values using positive and negative numbers.  Using order of operation, solve equation for y value.  Plot or graph x and y values.  Observe patterns in the relationship between the graph and the equation.  Compare and analyze the lines created.

Investigation/Exploration of the Problem

a.       Write an equation. Graph.  If f(x) and g(x) are parallel then they must have the same slope: a=c and b≠d.

b.      Write an equation. Graph.  If f(x) and g(x) are perpendicular then a and b are opposite reciprocals of each other.

c.       Write an equation. Graph.  If f(x) does not cross the x-axis then it is a horizontal line that has a slope with a value of 0.

d.      Write an equation. Graph.  If g(x) is vertical then x = c.

e.       Write an equation. Graph.  If f(x) and g(x) have the same y-intercept then b = d.

Extensions of the Problem

Discuss possible extensions for the problem and explore/investigate at least one of the extensions you discussed.

Author & Contact
llaster@rockdale.k12.ga.us

Link(s) to resources, references, lesson plans, and/or other materials

http://www.purplemath.com/modules/graphing.htm