Formulas for Linear Functions Lesson 1 4 What

What Do You Know about These Forms of Linear Equations? Slope Intercept form Standard

Slope and Y-Intercept • Consider y = m * x + b • The

Slope and Y-Intercept • Considering y = m * x + b • The

Slope and Y-Intercept • The function y = (2/3) * x + 5 •

Slope • When slope = • Try y = -7 x – 3 (predict

Graphing a Function • y = -7 x – 3 • Do the slope

Creating a Function from a Table • Determine slope by using Answer: x y

Creating a Function from a Table • Now we know slope m = 3/2

Creating a Function from a Table • Double check results • Substitute a different

Finding Formulas from Verbal Description • Read exercise 40, pg 34 of text •

Using a Graph to Find a Formula • Given a graph (2, 7) with

Assignment • Lesson 1. 4 • Page 32 • Exercises 1 – 9, 11,

Slides: 13

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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 2

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 3

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 Y 1 (2/3) * x + 5 Predict what the graph will look like before you specify F 2, 6 for standard zoom 4

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

Slope • When slope = • Try y = -7 x – 3 (predict the results before you graph) 6

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

Creating a Function from a Table • Determine slope by using Answer: x y 3 7 4 8. 5 5 10 6 11. 5 8

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 9

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 10

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? 11

Using a Graph to Find a Formula • Given a graph (2, 7) with two points • (8, 3. 4) • • Use the points to determine slope, m • Substitute (x, y) from one of points to find b • Answer: 12

Assignment • Lesson 1. 4 • Page 32 • Exercises 1 – 9, 11, 13, 15, 17, 19, 21, 23, 29, 37, 41 13