Graphing Linear Equations and Functions Chapter 4 Notes Graphing Linear Equations and Functions

4.1 Coordinates and Scatter Plots Objectives: -Plot points in a coordinate plane -Draw scatter plots and make predictions about the data

Terms Coordinate Plane Ordered pair X-coordinate Y-coordinate

Labeling the Coordinate plane

Plotting Points Plot the following points (0,3) (-2, -1) (2,0) (4,5)

Locating Quadrants Find the quadrant of the following points (0,3) (-2, -1) (2,0) (4,5)

Making a Scatter Plot

4.2 Graphing Linear Equations Part1 Objectives: -Make a list of values for a given equation

Terms Solution of an Equation Function Form

Function Form Rewrite the equations in function form (y=mx+b) -3x + y = 12 2x + 3y = 6

Function Form Rewrite the equations in function form (y=mx+b) -x – y = 5 5x + 5y = 20

T-Charts Rules for t-Charts Equations must be in function form Choose numbers for x Substitute them in for x Solve for y Repeat to get a total of 3 values for your function

T-Charts Make a table of values(T-Chart) for each function Y = -2x – 6 y = 3(6x – 1) X Y X Y

T-Charts Make a table of values(T-Chart) for each function Y = 3x - 5 y = 7 – 4x X Y X Y

Special Cases When the equation has an X but no Y Ex: x = 5 When the equation has a y but no x Ex: y = 8

4.2 Graphing Linear Equations Part2 Objectives: -Graph linear equations and make t- charts

T-Charts Rules for t-Charts Equations must be in function form Choose numbers for x Substitute them in for x Solve for y Graph the values

Graphing Y = 4x – 2 y = 2(x – 1) X Y X Y

Graphing 2x + 2y = 10 5x – 7 = 5y X Y X Y

4.3 Quick Graphs Using Intercepts Objectives: -Find the x and y intercepts -graph a linear equation using the x and y intercepts

Terms X- intercept Y- intercept

Finding the x-intercept X-intercepts always have ordered pairs in the form (#,0) To find the x-intercept you plug 0 in for y and solve for x.

Finding the y-intercept y-intercepts always have ordered pairs in the form (0,#) To find the y-intercept you plug 0 in for x and solve for y.

Practice Given the x and y intercepts graph the equation x-intercept = 2; x-intercept = -4; y-intercepts = -3 y-intercepts = 5

Finding x and y -intercept 5x + 4y = -20 6x – y = 6

Finding x and y -intercept -3x + y = -6 3x – y = -2

Objectives: -Find the slope of a line given 2 pts

Terms Slope Rate of change

Finding Slope form a Graph B

Finding Slope with a Formula Slope = change in y change in x

Special cases #/0 means slope = undefined (U) 0/# means slope = 0

Practice (2,3)(4,-5) (1,-5)(-5,2) (3,6)(3,0) (0,5)(7,5)

Practice (4,1)(6,-3) (2,2)(-3,5) (-6,-1)(-6,-4) (0,-10)(-4,0)

White Board Practice One person from each row get white boards and accessories

4.6 Quick Graphs Using Slope Intercept Objectives: -Graph a linear equation in slope intercept form

Terms Slope-intercept form Parallel lines Perpendicular Lines

Locating slope and intercept Given an equation in y=mx+b form m=slope (pattern) b= y-intercept (start pt.) Slope must be a fraction !!!

How it works 1st you start on the y axis at the b value 2nd you use your slope to rise and run from the b value

Practice Graph each of the following and tell the slope and intercept Y = 2x – 3 Y= -3x – 2 Y= ½ x + 5

Practice Graph each of the following and tell the slope and intercept Y= 2/3x – 1 Y= 2x 2y + 3x = 6