Chapter 1 Review Linear Relations

1. Chapter 1 ReviewLinear Relations

2. Finding the point of intersection of two lines graphically Method 1 • Find slope and y-intercept • Equation must be y = mx + b form • m is slope, b is y-intercept Example slope = rise = y – intercept = run = • start at ( , ) go (other eq’n y = 2x + 1)

3. Method 2 • Find x and y intercepts • Equation may be in any form  Example x-inty-int y = 0 x = 0 • Plot the two points and connect

4. Finding the Point of Intersection POI is approximately (-3.2, - 1.8)

5. Finding the POI using Substitution • Isolate 1 variable in 1 equation • Sub into other equation • Solve • Sub answer into original equation and calculate

6. Example 3x + 2y = 8 -1x + 4y = 9

7. Finding the POI using Elimination • Use multiplication to get one variable having the same number in both equations. (They can have different signs) • If the signs for the variable with the same number are the same, subtract the two equations, otherwise add • Sub answer into an original equation and solve

8. Example 3x + 2y = 8 -1x + 4y = 9

9. Linear Relations Review Questions • Find the point of intersection of two lines graphically – • Ch review p.121, #3 and 4 & Ch. review test p.137, #1 • Find the point of intersection using substitution – • Ch review p.128, #16 & 17 & Ch review test p.137, #2 • Find the point of intersection using elimination – • Ch review p.131#21, 22 & Ch review test p.137, #3 • Draw a graph representing a system of equations with no solution, or one solution, or an infinite number of solutions – • Ch. review p.123, #6 & Ch. review test p.137, #9 • Set-up and solve word problems – • Ch review p.121, #5, p.123, #7-10, p.125, #12-14, p.128, #18-20 & p.131, #23-25 & Ch review test p.137,#5 – 7 • Find the equation of a line, given the slope “M” and a point on the line that isn’t the y intercept – • Used in Chapter 2 verifying geometric properties • Find the equation of a line, given two points – • Used in Chapter 2 verifying geometric properties