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)

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

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

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

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

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

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