1. Students will be able to write a linear equation in standard form. ANSWER 1.(1, 4), (6, –1) y + 2 = 3(x + 1) or y – 7 = 3(x – 2) y – 4 = –(x – 1) or y + 1 = –(x – 6) 2.( –1, –2), (2, 7) Write an equation in point-slope form of the line that passes through the given points. Warm-Up 3. A store rents 3 DVDs for $5, plus $3 for each additional DVD. Find the cost of renting 20 DVDs. $56 ANSWER

2. Students will be able to write a linear equation in standard form. Review Homework

3. Students will be able to write a linear equation in standard form. ANSWER y + 4 = –2(x –6) Daily Homework Quiz Write an equation in point-slope form of the line that passes through (6, – 4) and has slope 2. 1. Write an equation in point-slope form of the line that passes through (–1, –6) and (3,10). 2. ANSWER y + 6 = 4(x + 1) or y –10 = 4(x–3) A travel company offers guided rafting trips for $875 for the first three days and $235 for each additional day. Write an equation that gives the total cost (in dollars) of a rafting trip as a function of the length of the trip. Find the cost for a 7 -day trip. 3. ANSWER C = 235t + 170, where C is total cost and t is time (in days); $1815

4. Students will be able to write a linear equation in standard form. Methods to Represent Linear Functions Slope Intercept Form: y = mx + b Point-Slope Form: y – y 1 = m(x – x 1 ) m = slope (x 1, y 1 ) = point on the line Standard Form: Ax + By = C A, B, and C are real numbers. Useful to model real life situations…. Not useful for graphing

5. Students will be able to write a linear equation in standard form. y = 2x – 9 y = 6 - 5x y = 9 + x y + 1 = 3(x + 1) y – 2 = 5(x – 11) Write these equations in standard form. EXAMPLE 1 Write equations in standard form 2x – y = 9 5x + y = 6 x – y = -9 -3x + y = 2 -5x + y = -53

6. Students will be able to write a linear equation in standard form. SOLUTION y – y 1 = m(x – x 1 ) Calculate the slope. STEP 1 EXAMPLE 2 Write an equation from a graph – 3– 3m =m = 1 – (–2) 1 –2 = 3 –1 = Write an equation in point-slope form. Use (1, 1). Write point-slope form. y – 1 = – 3(x – 1) Substitute 1 for y 1, 23 for m and 1 for x 1. Write an equation in standard form of the line shown. STEP 2

7. Students will be able to write a linear equation in standard form. Rewrite the equation in standard form. EXAMPLE 2 Write an equation from a graph 3x + y = 4 Simplify. Collect variable terms on one side, constants on the other. STEP 3

8. Students will be able to write a linear equation in standard form. SOLUTION y – y 1 = m(x – x 1 ) Calculate the slope. STEP 1 EXAMPLE 2 Write an equation from a graph 2 m =m = –3–(–1) 2 –3 = –2 –1 = Write an equation in point-slope form. Use (3, –1). Write point-slope form. y + 1 = 2(x – 3) Substitute 3 for x 1, –1 for y 1 and 2 for m. STEP 2 GUIDED PRACTICE for Examples 1 and 2 Write an equation in standard form of the line through (3,–1) and (2, – 3). 2

9. Students will be able to write a linear equation in standard form. Rewrite the equation in standard form. EXAMPLE 2 Write an equation from a graph – 2x + y = –7 Simplify. Collect variable terms on one side, constants on the other. STEP 3 GUIDED PRACTICE for Examples 1 and 2

10. Students will be able to write a linear equation in standard form. SOLUTION EXAMPLE 3 Write an equation of a line Write an equation of the specified line. The y- coordinate of the given point on the blue line is –4. This means that all points on the line have a y- coordinate of –4. An equation of the line is y = –4. a.a. The x- coordinate of the given point on the red line is 4. This means that all points on the line have an x- coordinate of 4. An equation of the line is x = 4. b.b. Blue line a.a. Red line b.b.

11. Students will be able to write a linear equation in standard form. Simplify. Find the value of A. Substitute the coordinates of the given point for x and y in the equation. Solve for A. STEP 1 SOLUTION EXAMPLE 4 Find the missing coefficient in the equation of the line shown. Write the completed equation. Ax + 3y = 2 A(–1) + 3(0) = 2 –A = 2 A = – 2 Write equation. Substitute – 1 for x and 0 for y. Divide by – 1. EXAMPLE 3EXAMPLE 4 Complete an equation in standard form

12. Students will be able to write a linear equation in standard form. EXAMPLE 4 Complete an equation in standard form Complete the equation. – 2x + 3y = 2 Substitute – 2 for A. STEP 2

13. Students will be able to write a linear equation in standard form. SOLUTION Write equations of the horizontal and vertical lines that pass through the given point. The y- coordinate of the given point is –9. This means that all points on the line have a y- coordinate of –9. An equation of the line is y = –9. The x- coordinate of the given point is –8. This means that all points on the line have an x -coordinate of –8. An equation of the line is x = –8. GUIDED PRACTICE for Examples 3 and 4 3. (–8, –9) STEP 1 STEP 2

14. Students will be able to write a linear equation in standard form. SOLUTION The y- coordinate of the given point is –5. This means that all points on the line have a y- coordinate of –5. An equation of the line is y = –5. The x- coordinate of the given point is 13. This means that all points on the line have an x -coordinate of 13. An equation of the line is x = 13. GUIDED PRACTICE for Examples 3 and 4 Write an equation of the horizontal and vertical lines that pass through the given point. 4. (13, –5) STEP 1 STEP 2

15. Students will be able to write a linear equation in standard form. Simplify. Find the value of B. Substitute the coordinates of the given point for x and y in the equation. Solve for B. STEP 1 SOLUTION EXAMPLE 4 Complete an equation in standard form Find the missing coefficient in the equation of the line that passes through the given point. Write the completed equation. –4x + By = 7 –4(–1) + B(1) = 7 B = 3 Write equation. Substitute –1 for x and 1 for y. EXAMPLE 3 Write an equation of a line GUIDED PRACTICE for Examples 3 and 4 5. –4x+By = 7, (–1,1)

16. Students will be able to write a linear equation in standard form. EXAMPLE 4 Complete an equation in standard form Complete the equation. – 4x + 3y = 7 Substitute 3 for B. STEP 2 GUIDED PRACTICE for Examples 3 and 4

17. Students will be able to write a linear equation in standard form. Real Life Example Standard Form: Ax + By = C Example You have $50 to spend at a used book store. Paperbacks (x): $1, Hardcovers (y) $4 1x + 4y = 50 If I want to buy 7 hardcover books, how many paperback books could I buy? 1x + 4(7) = 50 -28 -28 x = 22

18. Students will be able to write a linear equation in standard form. Simplify. Find the value of A. Substitute the coordinates of the given point for x and y in the equation. Solve for A. STEP 1 SOLUTION EXAMPLE 4 Complete an equation in standard form Ax + y = –3 A ( 2 ) + 1 1 = – 3 2A= –14 Write equation. Substitute 2 for x and 11 for y. EXAMPLE 3 Write an equation of a line GUIDED PRACTICE for Examples 3 and 4 Divide each side by 2. A= –7 Find the missing coefficient in the equation of the line that passes through the given point. Write the completed equation. 6. Ax+y = –3, (2, 11)

19. Students will be able to write a linear equation in standard form. EXAMPLE 4 Complete an equation in standard form Complete the equation. – 7x +y = –3 Substitute –7 for A. STEP 2 GUIDED PRACTICE for Examples 3 and 4

20. Students will be able to write a linear equation in standard form. Library EXAMPLE 5 Your class is taking a trip to the public library. You can travel in small and large vans. A small van holds 8 people and a large van holds 12 people. Your class could fill 15 small vans and 2 large vans. b. Graph the equation from part ( a ). c. List several possible combinations. Solve a multi-step problem Write an equation in standard form that models the possible combinations of small vans and large vans that your class could fill. a.a.

21. Students will be able to write a linear equation in standard form. SOLUTION a. Write a verbal model. Then write an equation. Because your class could fill 15 small vans and 2 large vans, use (15, 2) as the s - and l -values to substitute in the equation 8s + 12l = p to find the value of p. 8(15) + 12(2) = p Substitute 15 for s and 2 for l. 144 = p Simplify. Substitute 144 for p in the equation 8s + 12l = p. EXAMPLE 5 Solve a multi-step problem 8s l p12+ =

22. Students will be able to write a linear equation in standard form. Substitute 0 for s. 8(0) + 12l = 144 l = 12 Substitute 0 for l. s = 18 8s + 12(0) = 144 ANSWER The equation 8s + 12l = 144 models the possible combinations. b. Find the intercepts of the graph. 8s + 12(0) = 144 EXAMPLE 5 Solve a multi-step problem

23. Students will be able to write a linear equation in standard form. 8s + 12(0) = 144 EXAMPLE 5 Solve a multi-step problem Plot the points (0, 12) and (18, 0). Connect them with a line segment. For this problem only nonnegative whole-number values of s and l make sense. The graph passes through (0, 12), (6, 8),(12, 4), and (18, 0). So, four possible combinations are 0 small and 12 large, 6 small and 8 large, 12 small and 4 large, 18 small and 0 large. c.

24. Students will be able to write a linear equation in standard form. EXAMPLE 5 Solve a multi-step problem EXAMPLE 5 Solve a multi-step problem GUIDED PRACTICE for Example 5 7. WHAT IF? In Example 5, suppose that 8 students decide not to go on the class trip. Write an equation that models the possible combinations of small and large vans that your class could fill. List several possible combinations.

25. Students will be able to write a linear equation in standard form. SOLUTION Write a verbal model. Then write an equation. 8 students decide not to go on the class trip, so the class could fill 14 small vans and 2 large vans. Because your class could fill 14 small vans and 2 large vans, use (14, 2) as the s - and l -values to substitute in the equation 8s + 12l = p to find the value of p. 8(14) + 12(2) = p Substitute 14 for s and 2 for l. 136 = p Simplify. Substitute 136 for p in the equation 8s + 12l = p. EXAMPLE 5 Solve a multi-step problem EXAMPLE 5 Solve a multi-step problem GUIDED PRACTICE for Example 5 8s l p12+ = STEP 1

26. Students will be able to write a linear equation in standard form. Substitute 0 for s. 8(0) + 12l = 136 Substitute 0 for l. s = 17 8s + 12(0) = 136 ANSWER The equation 8s + 12l = 136 models the possible combinations. Find the intercepts of the graph. 8s + 12(0) = 144 EXAMPLE 5 Solve a multi-step problem GUIDED PRACTICE for Example 5 l = 11 4 12 STEP 2

27. Students will be able to write a linear equation in standard form. 8s + 12(0) = 144 Plot the point (0,11 ) and (17, 0). connect them with a line segment. For this problem only negative whole-number values of s and l make sense. 4 12 The graph passes through (17, 0), (14, 2), (11, 4), (8, 6), (5, 8) and (2, 10). So, several combinations are 17 small, 0 large; 14 small 2 large ; 11 small, 4 large; 18 small, 6 large ; 5 small, 8 large; 2 small, 10 large. STEP 3 GUIDED PRACTICE for Example 5