Chapter 1 ReviewLinear Relations

Finding the point of intersection of two lines graphicallyMethod 1Find slope and y-interceptEquation must be y = mx + b formm is slope, b is y-intercept

Example

slope = rise =

y – intercept = run =

start at ( , ) go (other eq’n y = 2x + 1)

432 xy

Method 2Find x and y interceptsEquation may be in any form 

Example  x-int y-inty = 0 x = 0

 

Plot the two points and connect

623 yx

Finding the Point of Intersection

432 xy

623 yx

POI is approximately (-3.2, - 1.8)

Finding the POI using SubstitutionIsolate 1 variable in 1 equationSub into other equationSolveSub answer into original equation and

calculate

Example 3x + 2y = 8

-1x + 4y = 9

Finding the POI using EliminationUse 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

Example 3x + 2y = 8

-1x + 4y = 9

Linear Relations Review QuestionsFind the point of intersection of two lines graphically –

Ch review p.121, #3 and 4 & Ch. review test p.137, #1Find the point of intersection using substitution –

Ch review p.128, #16 & 17 & Ch review test p.137, #2Find the point of intersection using elimination –

Ch review p.131#21, 22 & Ch review test p.137, #3Draw 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 – 7Find 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