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5.4 Write Linear Equations in Standard Form

5.4 Write Linear Equations in Standard Form. Students will write equations in standard form. Students will do assigned homework. Students will study vocabulary words. 2. (. – 1, – 2), (2, 7). Lesson 5.4, For use with pages 311-316.

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5.4 Write Linear Equations in Standard Form

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  1. 5.4 Write Linear Equations in Standard Form Students will write equations in standard form. Students will do assigned homework. Students will study vocabulary words.

  2. 2. ( –1, –2), (2, 7) Lesson 5.4, For use with pages 311-316 Write an equation in point-slope form of the line that passes through the given points. 1. (1, 4), (6, –1) y – 4 = –(x – 1) ory + 1 = –(x – 6) ANSWER ANSWER y + 2 = 3(x + 1) ory– 7 = 3(x– 2)

  3. Lesson 5.4, For use with pages 311-316 3.A store rents 3 DVDs for $5, plus $3 for each additional DVD. Find the cost of renting 20 DVDs. ANSWER $56

  4. 1. Write an equation in point-slope form of the line that passes through (6, –4) and has slope 2. ANSWER y + 4 = –2(x – 6) 2. Write an equation in point-slope form of the line that passes through (–1, –6) and (3, 10). y + 6 = 4(x + 1) ory –10 = 4(x–3) ANSWER Daily Homework Quiz For use after Lesson 5.3

  5. 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. ANSWER C = 235t + 170, where C is total cost and t is time (in days); $1815 Daily Homework Quiz For use after Lesson 5.3

  6. EXAMPLE 1 Write equivalent equations in standard form Write two equations in standard form that are equivalent to 2x – 6y =4. SOLUTION To write another equivalent equation, multiply each side by 0.5. To write one equivalent equation, multiply each side by 2. 4x – 12y =8 x – 3y = 2

  7. 1 – (–2) m= –3 = = 1 – 2 3 –1 Write an equation from a graph EXAMPLE 2 Write an equation in standard form of the line shown. SOLUTION STEP1 Calculate the slope. STEP2 Write an equation in point-slope form. Use (1, 1). y –y1=m(x –x1) Write point-slope form. y –1=–3(x –1) Substitute 1 for y1, 3 for m and 1 for x1.

  8. Write an equation from a graph EXAMPLE 2 STEP3 Rewrite the equation in standard form. 3x + y = 4 Simplify. Collect variable terms on one side, constants on the other.

  9. 1. Write two equations in standard form that are equivalent to x – y =3. ANSWER 2x – 2y =6, 3x – 3y = 9 EXAMPLE 1 for Examples 1 and 2 GUIDED PRACTICE

  10. 2. Write an equation in standard form of the line through (3, –1) and (2, –3). ANSWER –2x + y = –7 Write an equation from a graph EXAMPLE 2 for Examples 1 and 2 GUIDED PRACTICE

  11. Write an equation of the specified line. a. b. Blue line Red line a. 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. 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. EXAMPLE 3 Write an equation of a line SOLUTION

  12. Find the missing coefficient in the equation of the line shown. Write the completed equation. Complete an equation in standard form EXAMPLE 4 EXAMPLE 3 EXAMPLE 4 SOLUTION STEP1 Find the value of A. Substitute the coordinates of the given point for xandyin the equation. Solve forA. Ax + 3y = 2 Write equation. A(–1) + 3(0) = 2 Substitute –1 for x and 0 for y. Simplify. –A = 2 A = –2 Divide by –1.

  13. Complete an equation in standard form EXAMPLE 4 STEP2 Complete the equation. –2x + 3y = 2 Substitute –2 for A.

  14. y=–9, x= –8 ANSWER for Examples 3 and 4 GUIDED PRACTICE Write equations of the horizontal and vertical lines that pass through the given point. 3. (–8, –9)

  15. y=–5, x= 13 ANSWER for Examples 3 and 4 GUIDED PRACTICE Write equations of the horizontal and vertical lines that pass through the given point. 4. (13, –5)

  16. ANSWER 3; –4x + 3y = 7 Complete an equation in standard form EXAMPLE 4 EXAMPLE 3 for Examples 3 and 4 Write an equation of a line GUIDED PRACTICE Find the missing coefficient in the equation of the line that passes through the given point. Write the completed equation. 5. –4x + By = 7, (–1, 1)

  17. ANSWER –7; –7x +y = –3 Complete an equation in standard form EXAMPLE 4 EXAMPLE 3 for Examples 3 and 4 Write an equation of a line GUIDED PRACTICE 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)

  18. a. Write an equation in standard form that models the possible combinations of small vans and large vans that your class could fill. Solve a multi-step problem EXAMPLE 5 LIBRARY 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.

  19. 8 s + 12 p l = Solve a multi-step problem EXAMPLE 5 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=pto find the value of p. Substitute15forsand2forl. 8(15) + 12(2) = p 144 = p Simplify. Substitute 144 for pin the equation 8s+12l = p.

  20. ANSWER The equation 8s+12l=144 models the possible combinations. Solve a multi-step problem EXAMPLE 5 b. Find the intercepts of the graph. Substitute0fors. 8(0) + 12l = 144 l = 12 Substitute 0 for l. 8s + 12(0) = 144 s = 18

  21. c. 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. Solve a multi-step problem EXAMPLE 5 Plot the points (0, 12) and (18, 0). Connect them with a line segment. For this problem only nonnegative whole-number values of sandlmake sense.

  22. ANSWER 8s + 12l= 136; 17 small, 0 large; 14 small, 2 large; 11 small, 4 large; 8 small, 6 large; 5 small, 8 large; 2 small, 10 large Solve a multi-step problem EXAMPLE 5 for Example 5 GUIDED PRACTICE Solve a multi-step problem 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.

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