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Find the slope of the line that passes through the points.

Learn how to find slopes, write equations for lines using y-intercept and slope, and solve multi-step problems involving linear functions. Practice guided exercises and standardized test examples. Improve your math skills!

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Find the slope of the line that passes through the points.

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  1. 1 2 Find the slope of the line that passes through the points. 1. (2, –1), (4, 0) ANSWER 2. (–1, –3), (1, 5) ANSWER 4

  2. Find the slope of the line that passes through the points. 3.A landscape architect charges $75 for a consulting fee and $30 per hour. Write an equation that shows the cost C as a function of time t (in hours). ANSWER C = 30t + 75

  3. EXAMPLE 1 Use slope and y-intercept to write an equation Write an equation of the line with a slope of –2 and a y-intercept of 5. y =mx + b Write slope-intercept form. y =–2x +5 Substitute –2 form and 5 for b.

  4. y =–x+ 3 y =–x+ 3 y =–x+ 1 y = 3x + D C B A 2 5 2 2 2 –2 5 5 2 5 The slope of the line is . – = = 5 rise 5 run 2 y= –x+3 2 5 Substitute– for mand3forb. 5 EXAMPLE 2 Standardized Test Practice Which equation represents the line shown? The line crosses the y-axis at (0, 3). So, they-intercept is 3. y =mx +b Write slope-intercept form.

  5. ANSWER The correct answer is A. B D C A EXAMPLE 2 Standardized Test Practice

  6. ANSWER y = 8x – 7 for Examples 1 and 2 GUIDED PRACTICE Write an equation of the line with the given slope and y-intercept. 1.Slope is 8; y-intercept is–7.

  7. 2. Slope is ; y intercept is –3. ANSWER 3 4 3 x– 3 y = 4 for Examples 1 and 2 GUIDED PRACTICE Write an equation of the line with the given slope and y-intercept.

  8. EXAMPLE 3 Write an equation of a line given two points Write an equation of the line shown.

  9. y2 – y1 –1 – (–5) 4 m = = = x2 – x1 3 – 0 3 Substitute for mand 5 for b. 4 4 y = x – 5 3 3 EXAMPLE 3 Write an equation of a line given two points SOLUTION STEP 1 Calculate the slope. STEP 2 Write an equation of the line. The line crosses the y-axis at (0, –5). So, the y-intercept is –5. y =mx +b Write slope-intercept form.

  10. y2 – y1 17 – 5 12 m 3 = = = = x2 – x1 4 – 0 4 Write a linear function EXAMPLE 4 Write an equation for the linear function fwith the values f(0) = 5 andf(4) = 17. SOLUTION STEP 1 Write f(0) = 5 as (0, 5) and f (4)= 17 as (4, 17). STEP 2 Calculate the slope of the line that passes through (0, 5) and (4, 17).

  11. ANSWER The function is f(x) = 3x + 5. Write a linear function EXAMPLE 4 STEP 3 Write an equation of the line. The line crosses the y-axis at (0, 5). So, the y-intercept is 5. y =mx + b Write slope-intercept form. y =3x + 5 Substitute 3 for mand 5 for b.

  12. 1 x + 1 – y = ANSWER 2 GUIDED PRACTICE for Examples 3 and 4 3. Write an equation of the line shown.

  13. 4. Write an equation for the linear functionf with the given values. ANSWER 3 y =x – 2 4 GUIDED PRACTICE for Examples 3 and 4 f(0) = –2, f(8) = 4

  14. Write an equation for the linear function fwith the given values. 5. – ANSWER y =x + 5 1 3 GUIDED PRACTICE for Examples 3 and 4 f(–3) = 6, f(0) = 5

  15. a. Write an equation that gives the total cost of an album as a function of studio time (in hours). b. Find the total cost of recording an album that takes 10 hours of studio time. EXAMPLE 5 Solve a multi-step problem Recording Studio A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs an additional $35 per hour.

  16. a. The cost changes at a constant rate, so you can write an equation in slope-intercept form to model the total cost. EXAMPLE 5 Solve a multi-step problem SOLUTION

  17. C 50 = t 35 + EXAMPLE 5 Solve a multi-step problem STEP 1 Identify the rate of change and the starting value. Rate of change, m: cost per hour Starting value, b: initial fee STEP2 Write a verbal model. Then write the equation.

  18. CHECK Use unit analysis to check the equation. dollars dollars= hour hours+dollars ANSWER The total cost Cis given by the function C = 35t + 50 where tis the studio time (in hours). ANSWER The total cost for 10 hours of studio time is $400. EXAMPLE 5 Solve a multi-step problem b. Evaluate the function for t = 10. C = 35(10) + 50 = 400 Substitute 10 for tand simplify.

  19. WHAT IF?In Example 5, suppose the recording studio raises its initial fee to $75 and charges $40 per hour for studio time. 6. Write an equation that gives the total cost of an album as a function of studio time (in hours). a. ANSWER C = 40t +75 for Example 5 GUIDED PRACTICE

  20. Find the total cost of recording an album that takes 10 hours of studio time. b. ANSWER $475 for Example 5 GUIDED PRACTICE

  21. 1. Write an equation of the line with a slope of –4 and a y-intercept of 1. ANSWER ANSWER ANSWER y = –4x + 1 y = –x – 8 y = 3x + 6 2. 3. (–9, 1), (0, –8) (–4, –6), (0, 6) Daily Homework Quiz Write an equation of the line that passes through the given points.

  22. 4. Write an equation for the linear function f with f(0) = –4 and f(–1) = –9. ANSWER y = 5x – 4 5. An electronics game store sells used games for $12.99 with a $20 membership fee. Write an equation that gives the total cost to become a member and buy games as a function of the number of games that are purchased. Then find the cost for 6 games. ANSWER C = 12.99g + 20 where C is total cost and g is the number of games; $97.94 Daily Homework Quiz

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