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Graphing Family of Lines: Guided Practice

Learn how to graph different lines in the form y=mx+b using a calculator. Understand the concept of slope (m) and y-intercept (b) and apply it to real-life examples. Interpret graphs & equations to analyze data effectively.

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Graphing Family of Lines: Guided Practice

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  1. Guided Practice Graph the following family of lines using a graphing calculator: y = 3x + 2 y = 5x + 2 y = -4 x + 2 Graph the following family of lines using a graphing calculator: y = 3x + 2 y = 3x - 4 y = 3x NOTICE: All of these equations are written in the form: y = mx+b

  2. The Slope-Intercept Form of a line:y = mx + b

  3. Given: y = mx + b • m represents the __________ of the line. • b represents the ___________ - the point where the line crosses the __________.

  4. Given: y = mx + b • m represents the SLOPE of the line. • b represents the Y-INTERCEPT - the point where the line crosses the Y-AXIS.

  5. Follow-Up Activity

  6. EXAMPLE 1 Who cares about this stuff? Return to Mc Arthur Mall 1. You have been working at McArthur Shopping Mall for several months. Your retail job still pays $150.00 plus a 10% commission of your sales per week. In your first three weeks you sold $700 of merchandise, then $300 and $1500 worth of merchandise. a. Plot these three salaries as points on a linear graph. b. Determine the linear equation that models how your pay is calculated. Graph/sketch this equation. c. How are the graphs from the two steps above related? Discuss. 2. Your supervisor comes to you and offers you a new pay scale where you earn $200 plus 7% commission of your sales per week. Should you accept the offer? Why? Why not?

  7. r m C = + b EXAMPLE 1 Solve a multi-step problem SOLUTION STEP 1 Identify the rate of change and starting value. Rate of change, m: entry fee per race Starting value, b: track membership cost STEP 2 Write a verbal model. Then write an equation.

  8. y2 – y1 170 – 125 45 m = = = 15 = x2 – x1 3 8 – 5 EXAMPLE 1 Solve a multi-step problem STEP 3 Calculate the rate of change. This is the entry fee per race. Use the slope formula. Racer 1 is represented by (5, 125). Racer 2 is represented by (8, 170). STEP 4 Find the track membership cost b. Use the data pair (5, 125) for racer 1 and the entry fee per race from Step 3.

  9. ANSWER The track membership cost is $50. The entry fee per race is $15. EXAMPLE 1 Solve a multi-step problem C= mr+ b Write the equation from Step 2. 125 = 15(5) + b Substitute 15 for m, 5 for r, and 125 for C. 50 = b Solve for b.

  10. EXAMPLE 2 Solve a multi-step problem SALES CLERK Joe is a sales clerk in a department store and his gross pay for the month is determined by the value of the merchandise that he sells that month. One month he had $12000 in sales and his gross pay was $1960. The next month he had only $9000 in sales and his gross pay fell to $1720.

  11. EXAMPLE 2 Solve a multi-step problem SOLUTION • Write a linear equation giving Joe's gross pay y in terms of his monthly sales amount x. • We know two points on the graph of the equation: (12000,1960) and (9000,1720). • The slope of the line is m = (1960-1720)/(12000-9000) = 0.08.

  12. EXAMPLE 2 Solve a multi-step problem SOLUTION Using the second point (9000,1720) and the slope m = 0.08 we find the Point-Slope form of the equation of the line to be y - 1720 = 0.08 (x - 9000). Solving for y yields the Slope-Intercept form: y = 0.08 x + 1000.

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