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1、5.4 Write Linear Equations in Standard FormStudents will write equations in standard form.Students will do assigned homework.Students will study vocabulary words. Lesson 5.4, For use with pages 311-316ANSWERANSWER1. (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、 (2, 7)Write an equation in point-slope form of the line that passes through the given points. 3. A store rents 3 DVDs for $5, plus $3 for each additional DVD. Find the cost of renting 20 DVDs. Lesson 5.4, For use with pages 311-316ANSWER $56 ANSWER y + 4 = 2(x 6)Daily Homework Quiz For use after Le
3、sson 5.3Write 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(x3) Daily Homework Quiz For use after Lesson 5.3A travel company of
4、fers 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. ANSWERC = 235t + 170, where C is total cost and t is ti
5、me (in days); $1815 To write another equivalent equation, multiply each side by 0.5.4x 12y = 8To write one equivalent equation, multiply each side by 2.SOLUTIONWrite two equations in standard form that are equivalent to 2x 6y = 4.EXAMPLE 1 Write equivalent equations in standard formx 3y = 2 SOLUTION
6、 y y1 = m(x x1)Calculate the slope.STEP 1EXAMPLE 2 Write an equation from a graph3m = 1 (2)1 2 = 31 =Write an equation in point-slope form. Use (1, 1).Write point-slope form.y 1 = 3(x 1) Substitute 1 for y 1, 3 for m and 1 for x1. Write an equation in standard form of the line shown.STEP 2 Rewrite t
7、he equation in standard form.EXAMPLE 2 Write an equation from a graph3x + y = 4 Simplify. Collect variable terms on one side, constants on the other.STEP 3 EXAMPLE 1GUIDED PRACTICE for Examples 1 and 2Write two equations in standard form that are equivalent to x y = 3.1. 2x 2y = 6, 3x 3y = 9ANSWER E
8、XAMPLE 2 Write an equation from a graphGUIDED PRACTICE for Examples 1 and 2Write an equation in standard form of the line through (3, 1) and (2, 3).2. 2x + y = 7ANSWER SOLUTIONEXAMPLE 3 Write an equation of a lineWrite an equation of the specified line.The y-coordinate of the given point on the blue
9、 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. 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. Blue linea. Red lineb. Simp
10、lify.Find the value of A. Substitute the coordinates of the given point for x and y in the equation. Solve for A.STEP 1SOLUTION EXAMPLE 4Find the missing coefficient in the equation of the line shown. Write the completed equation.Ax + 3y = 2A(1) + 3(0) = 2A = 2 A = 2 Write equation.Substitute 1 for
11、x and 0 for y.Divide by 1. 3 Complete an equation in standard form EXAMPLE 4 Complete an equation in standard formComplete the equation.2x + 3y = 2 Substitute 2 for A.STEP 2 Write equations of the horizontal and vertical lines that pass through the given point.GUIDED PRACTICE for Examples 3 and 43.
12、(8, 9) y = 9, x = 8ANSWER GUIDED PRACTICE for Examples 3 and 44. (13, 5) y = 5, x = 13ANSWERWrite equations of the horizontal and vertical lines that pass through the given point. EXAMPLE 4 Complete an equation in standard formFind the missing coefficient in the equation of the line that passes thro
13、ugh the given point. Write the completed equation.3 Write an equation of a lineGUIDED PRACTICE for Examples 3 nd 45. 4x + By = 7, (1, 1)ANSWER 3; 4x + 3y = 7 EXAMPLE 4 Complete an equation in standard form3 Write an equation of a lineGUIDED PRACTICE for Examples 3 nd 46. Ax + y = 3, (2, 11)Find the
14、missing coefficient in the equation of the line that passes through the given point. Write the completed equation.ANSWER 7; 7x +y = 3 LIBRARYEXAMPLE 5Your 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.
15、 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 problemWrite an equation in standard form that models the possible combinations of small vans and large vans that your class could fill.a. SOLUTIONa. Wri
16、te 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
17、equation 8s + 12l = p.EXAMPLE 5 Solve a multi-step problem8 s l p12+ = Substitute 0 for s.8(0) + 12l = 144l = 12Substitute 0 for l.s = 188s + 12(0) = 144ANSWERThe equation 8s + 12l = 144 models the possible combinations.b. Find the intercepts of the graph.EXAMPLE 5 Solve a multi-step problem EXAMPLE
18、 5 Solve a multi-step problemPlot 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 s
19、mall and 8 large, 12 small and 4 large, 18 small and 0 large.c. EXAMPLE 5 Solve a multi-step problemEXAMPLE 5 Solve a multi-step problemGUIDED PRACTICE for Example 57. 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.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 largeANSWER
WriteLinearEquationsinStandardForm54寫的線性方程的標準形式
