Chapter 4 Notes 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 n Coordinate Plane n Ordered pair n X-coordinate n Y-coordinate

Labeling the Coordinate plane

Plotting Points Plot the following points a. (0, 3) b. (-2, -1) c. (2, 0) d. (4, 5)

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

Making a Scatter Plot

4. 2 Graphing Linear Equations Part 1 Objectives: -Make a list of values for a given equation

Terms n Solution of an Equation n Function Form

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

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

T-Charts n 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 n Y = -2 x – 6 y = 3(6 x – 1) n X Y

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

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

4. 2 Graphing Linear Equations Part 2 Objectives: -Graph linear equations and make t- charts

T-Charts n 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 n Y = 4 x – 2 X Y y = 2(x – 1) X Y

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

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

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

Practice n n 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 n 5 x + 4 y = -20 n 6 x – y = 6

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

4. 4 Slope Objectives: -Find the slope of a line given 2 pts

Terms n Slope n Rate of change

Finding Slope form a Graph A B

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

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

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

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

White Board Practice n 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 n Slope-intercept form n Parallel lines n Perpendicular Lines

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

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

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

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