Formulas for Linear Functions Lesson 1.4

What Do You Know about These Forms of Linear Equations? Slope Intercept form Standard form Slope-Point form (h,k) a point on the line m = the slope Two Intercept form

Slope and Y-Intercept Consider y = m * x + b The m and b are called parameters they affect the appearance of the graph The m is the slope m > 0 line is up to the right m < 0 line is down to the right m = 0 horizontal line |m| large very steep line

Slope and Y-Intercept Considering y = m * x + b The b is the y-intercept Where on the y-axis, the line intersects On your calculator Go to Y= screen Enter at Y1 (2/3) * x + 5 Predict what the graph will look like before you specify F2, 6 for standard zoom

Slope and Y-Intercept The function y = (2/3) * x + 5 Slope = 2/3 (up to the right) Y-intercept = 5 •

Slope When slope = Try y = -7x – 3 (predict the results before you graph)

Graphing a Function y = -7x – 3 Do the slope and y-intercept agree with your prediction? y-intercept = -3

Creating a Function from a Table Determine slope by using x y 3 7 4 8.5 5 10 6 11.5 Answer:

Creating a Function from a Table Now we know slope m = 3/2 Use this and one of the points to determine y-intercept, b Substitute an ordered pair into y = (3/2)x + b x y 3 7 4 8.5 5 10 6 11.5

Creating a Function from a Table Double check results Substitute a different ordered pair into the formula Should give a true statement x y 3 7 4 8.5 5 10 6 11.5

Finding Formulas from Verbal Description Read exercise 40, pg 34 of text Profit y = ___ x + ______ where x is number of patrons? What does the slope mean? What does the y-intercept mean? How many patrons are needed to start making money? How could you represent patrons p = ____ x + _____ where x is the amount of profit?

Using a Graph to Find a Formula Given a graph with two points Use the points to determine slope, m Substitute (x,y) from one of points to find b Answer: (2,7) • (8, 3.4) •

Assignment Lesson 1.4 Page 32 Exercises 1 – 9, 11, 13, 15, 17, 19, 21, 23, 29, 37, 41