[Remember: In Standard Form, slope = -(A/B) and y-intercept = C/B.]

- Use the sliders and graph the equations to find and write the solution(s) of the following linear systems.

a.) 4x + 2y = 8 and -2x + 5y = -4

b.) -2x + 6y = 2 and -2x + 5y = 3

c.) x - 3y = -4 and 9x + 3y = -6

d.) 4x - 8y = 2 and 2x - 4y = -5

e.) x - 3y = 2 and 3x - 9y = 6

- Look at the lines in 1c and find a geometric relationship between them. Now calculate the slopes of those graphs and write them in fraction form. Find and explain the relationship between the slopes in 1c.
- Calculate the slopes and y-intercepts in 1d. What is the relationship between the lines?
- Explain why there is only one line in 1e. What is the solution? Now calculate and compare the slopes and y-intercepts in 1e and explain the effects on the system.

EPankowski, 4/10/2007, Created with GeoGebra Updated by S.H. Lapinski

Please direct questions and comments to HCPS Mathematics Specialist Henrico County Public Schools, 2009