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Write an equation in both slope-intercept form and standard form for the line.
6. Using the addition and multiplication properties of equality, show that the equation
10x + 35y = 70 is equivalent to y = − 27
x + 2.
Challenge Problem
7. Marshall likes to use interval training. He jogs at 200 meters per minute and runs 250 meters per minute. He runs 8 km every day. Write an equation in standard form. Let x represent the number of minutes of jogging and y represent the number of minutes of running for Marshall’s interval training.
1. Write the equation 6x + 3y = 12 in slope intercept form. (y = mx + b)
Solve each system of equations. If the system has no solution, write no solution. If a system has infinitely many solutions write infinitely many solutions.
2. y = 2x + 3
y = 3x – 4
3. y = 3x – 2x
y – x = 4
4. 4 + y = 4x
y = 4(x – 1)
5. 3 = 3x + y
– 3x + y = 8
6. 9 = 5x – y
–3x + y = 9
Challenge Problem
7. Write a system of two equations that has no solution. Describe what the graph of the system would look like.
Solve each system of equations using the substitution method. If the system has no solution, write no solution. If a system has infinitely many solutions, write infinitely many solutions.
2. x = 4y + 2
2x – 3y = 9
3. y = 2x
3x + y = 12
4. 3x + y = 5
4x + 2y = 20
5. 4x + 5 = y
4x – y = 8
6. y = 3x – 7 + x
7 = 4x – y
Challenge Problem
7. Write a system of equations that has (4, 5) as the solution.
1. The sum of two numbers is 25. Their difference is 9. What are the two numbers? Use a system of equations to find the two numbers.
2. A fire lookout is a person who looks for fire from the top of a structure known as a fire lookout tower. These towers are used in remote areas, often on mountain tops. From these towers, the fire lookouts have a good view of the surrounding terrain and are able to spot wildfires.
The grid shows the location of two lookout towers.
123456789
10
–5–4–3–2
10987654321 x
y
Tower 1
Tower 2
A fire breaks out. The fire lookout at Tower 1 sees the fire with a line-of-sight having
slope of – . The fire lookout at Tower 2 sees the fire with a line-of-sight having
slope of 1.
At the coordination center, exact coordinates of the fire are needed in order to find the optimal position for a water-bombing plane.
a. What is the y-intercept and slope of each line? b. Find the linear equations of the two lines. c. Find the coordinates of the fire.
3. Jones and Janes are two competing landscaping companies.
Jones charges $40 to come to the location and then $40 per hour.
Janes made a graph representing her company’s costs.
34032030028026024022020018016014012010080604020
543 82 71 6 x
y
Hours
Dollars
Two points on the graph are (0, 60) and (3, 150).
The horizontal axis shows the number of hours. The vertical axis shows the total cost.
a. Which company is less expensive for a 3-hour job? b. Draw the graph of Jones in the same coordinate system.c. What are the coordinates of the point of intersection of the two lines? d. What is the meaning of this point?
4. Points A, B, C, and D represent the locations of four airports.
1
2
3
4
5
–2
–154321–1–2–3–4 x
y
D
A
C
B
a. Find the slope of each line segment shown. b. Find the y-intercepts of each segment. c. Write the system of linear equations that will give you the coordinates
of the point of intersection of the two segments. d. Solve the system of equations.