1. Malcolm enters an 80km ultra-marathon race. His walking speed is 8km/h and running speed is 10km/h. Let x=hours walked and y=hours run. 2. The linear equation relating x and y is 8x + 10y = 80. 3. If Malcolm walked the entire race, it would take him 10 hours. If he ran the entire race, it would take 8 hours. 4. If he walks for 6 hours, he will need to run for 3.2 hours to complete the 80km race.

1. Name ____________________________
Unit 6 Practice #1
1. You purchase a new smartphone plan. The 5. The 8th Grade Leadership Council is selling
company charges you a monthly rate of $36 for tickets to the Sweetheart Dance. Tickets cost $5 per
unlimited talk and text, and an additional $7.50 for person or $8 per couple. They sold $320 worth of
each gigabyte of data used. Write a linear equation tickets. Write a linear equation to describe the
to show monthly cost as a function of data used. situation.
y = 7.5x + 36 5x + 8y = 320
How much would the plan cost if you use 6 GB of 6. Robert is buying pecans and cashews for a party.
data? He has $48 to spend. Pecans cost $6 per pound and
$81 cashews cost $4 per pound. Let x represent pounds
2. Brittany’s limousine service charges a flat fee of of pecans, and let y represent pounds of cashews.
$60 plus $50 per hour. Write a linear function to Write a linear equation to represents the situation.
show cost of a ride as a function of hours. 6x + 4y = 48
y = 50x + 60 How many pounds of cashews can Robert buy if he
What is the total cost of renting the limousine for 15 buys 6 pounds of pecans?
hours? 3 pounds
$810 7. What is the slope of the linear function? 7 or
3. Mariah began a fitness routine that involves
running. She records the number of miles she runs
x 1 2 3 4 5
each day. So far, she has run a total of 220 miles,
y -44 -37 -30 -23 -16
she runs an additional 6 miles every day. Write a
linear function to show total miles as a function of
days. 8. What is the slope of the linear function?
y = 6x + 220 (2, 8), (6, 16), (10, 24), (14, 32)…
What will be her total miles 60 days from now? 2 or
580 miles 9. Is the ordered pair (5, -3) a solution to the
4. The FCCLA sells cookies at break time to fund equation 4x + 3y = 11?
their activities. To make 150 cookies, they have Yes; 20 – 9 = 11
startup costs of $50 for cookie dough and wrappers. 10. Which expression represents a line with a
They sell each cookie for $1.50. Write a linear positive slope?
function, create a table and graph to describe the
profit they make from selling 11. Does the point (-2, -6) lie on the graph of the
cookies? equation 2x – y = 8?
y = 1.5x - 50 No; -4 – (-6) = 2
12. Find the x- and y-intercepts for the graph of the
equation: -3x + 5y = 30
x-int = -10; y-int = 6
x 20 40 60 80 100 13. Find the x- and y-intercepts for the graph of the
y -20 10 40 70 100 equation: 3x – 2y = 42
x-int = 14; y-int = -21
What is their profit if they sell all 150 cookies?
$175

2. Malcolm enters an ultra-marathon race of 80 Km.
His average walking speed is 8 Km/h, and his
average running speed is 10 Km/h.
Let x = Number of hours he walks
Let y = Number of hours he runs
14. Standard form equation: 8x + 10y = 80
15. Slope-intercept form equation: y =
16. How long will it take Malcolm to complete the
race if he walks the entire 80 Km?
10 hours
17. How long will it take if he runs the entire 80
Km?
8 hours Emma is running faster. Her slope is steeper. Emma is running at
18. If he walks for 6 hours, how long will he have a rate of 5 yds/sec, and Maggie is running at a reate of 2.5 yds/sec.
to run?
3.2 hours
s = 2.5t.
Maggie has a 30yd headstart. Emma catches, then passes Maggie
after 10seconds at the 50 yd point. Emma wins the 70 yd race in 14
seconds. Maggie finishes in 20 seconds.
Make up a story for the graph below.
Find the slope of the line that passes through the
given points.
21. (7, 11), (9, 15) Slope: __ _______
22. (4, 12), (7, 10) Slope: __ _______
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