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Formulas for Linear Functions

Formulas for Linear Functions. Lesson 1.4. Slope Intercept form. Standard form. Slope-Point form (h,k) a point on the line m = the slope. Two Intercept form. What Do You Know about These Forms of Linear Equations?. Slope and Y-Intercept. Consider y = m * x + b

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Formulas for Linear Functions

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  1. Formulas for Linear Functions Lesson 1.4

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

  3. 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

  4. 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

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

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

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

  8. Answer: Creating a Function from a Table • Determine slope by using

  9. Creating a Function from a Table • Now we know slope m = 3/2 • Use this and one ofthe points to determiney-intercept, b • Substitute an orderedpair into y = (3/2)x + b

  10. Creating a Function from a Table • Double check results • Substitute a different ordered pair into the formula • Should give a true statement

  11. 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?

  12. Using a Graph to Find a Formula • Given a graphwith two points • Use the points todetermine slope, m • Substitute (x,y) from one of points tofind b • Answer: (2,7) • (8, 3.4) •

  13. Assignment • Lesson 1.4 • Page 32 • Exercises1 – 9, 11, 13, 15, 17, 19, 21, 23, 29, 37, 41

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