A
What is the slope-intercept form?
y=mx+b
Decide if each equation has no solution, one solution, or infinitely many solutions.
-3x-5=-3x+10
No Solution
Determine whether the equation has no solution, one solution, or infinitely many solutions. Show each step of your work.
4(3x+5)=2(6x-4)
No Solution
Decide if each equation has no solution, one solution, or infinitely many solutions.
7x-8=7x-8
Infinitely Many Solutions
What does b stand for in the given equation y=mx+b?
y-intercept
Decide if each equation has no solution, one solution, or infinitely many solutions.
5x-4=3x+6
One Solution
x=5
Decide if each equation has no solution, one solution, or infinitely many solutions.
3x+4=4+3x
Infinitely Many Solutions
Graph presented on another screen.
The slope of segment JL is ____ to the slope of segment RT.
What is the slope-formula?
m=y2-y1/x2-x1
Write the equation of the line in slope-intercept form. Explain how you found the slope and the y-intercept. Enter your answer and your explanation in the space provided. (Graph presented on another screen)
y=-x+3
A chef is setting up a rectangular tabletop for a display.
The cost of setting up the sides of the tabletop is 15$ per foot.
The length of the rectangular tabletop will be 5 more feet than the width.
The chef wants to have a total cost of $900 for the setup.
Let w represent the width of the rectangular tabletop in feet. Which equation can be used to find the value of w?
A) 15 (w+5) = 900
B) 15 (4w+10) = 900
C) 15 (5w+5) = 900
D) 15 (5w+10) = 900
B) 15 (4w+10) = 900
Jessica runs a bakery that bakes custom cakes. The cost to bake cakes is proportional to the number of cakes she bakes. Jessica graphs a line that shows the cost per custom cake. Two points on the line are (3, 12) and (6, 24). What does the slope of the line mean in this situation?
A)The cost is $3 per cake.
B) The cost is $4 per cake.
C) The cost is $6 per cake.
D) The cost is $8 per cake.
C) The cost is $6 per cake.
Graph presented on another screen.
Use the ratios of the side lengths of triangle JLK and triangle RTS to explain your answer to Part A.
Enter your explanation in the space provided.
ratio: LK/TS = KJ/SR = LJ/TR
4/2 = 8/4
2=2
Sophia works in a store. She packs bags with things to fulfill customer orders. Sophia packed 6 full bags and 4 bags that were not full. Each of the 4 bags contained 2 fewer things than a full bag. The total number of things she packed was 142.
Which equation can be used to find t, the number of things in a full bag?
A. 6t+4(t−2)=142
B. 6t+(4−2)t=142
C. 6t+4t−2=142
D. (6t+4)(t−2)=142
A. 6t+4(t−2)=142
Graph presented on another screen.
A hot air balloon descends from an altitude of 2,000 feet at a constant rate of 90 feet per minute. The graph shows the altitude of the balloon over time. What is the equation of the hot air balloon’s line in slope-intercept form? What do the slope and y-intercept represent in this situation? Show your work.
y=-90x+2000
What is the value of k? Show your work.
5/6(4k-8)=3(2k+3)-7/3K
k=-47
What is the y-intercept of a line that passes through the points (1,3) and (5,7)? Show your work.
b=2
Sophia works in a store. She packs bags with things to fulfill customer orders. Sophia packed 6 full bags and 4 bags that were not full. Each of the 4 bags contained 2 fewer things than a full bag. The total number of things she packed was 142.
6t+4(t−2)=142
What is the number of things in one full bag?
15
Solve for t. Show your work.
5(3t-2)-20t=45(2-4t)
t=100/175 or 4/7
A chef is setting up a rectangular tabletop for a display.
The cost of setting up the sides of the tabletop is 15$ per foot.
The length of the rectangular tabletop will be 5 more feet than the width.
The chef wants to have a total cost of $900 for the setup.
15 (4w+10) = 900
What will be the width, w, of the rectangular tabletop? _________________
12.5 feet