OBJECTIVE: Students will be able to interpret the meaning of ______, the x-intercept, and the y-intercept from a graph, table, equation, or situation.
Notes:
Slope-intercept Form: y = mx + b or y = b + mx1. m =
2. b =
3. eqn: / Slope: the rate of change.
Key words: per, each, every
4. The eagle descends ______per ______.
Y-intercept: starting point or beginning
Key words: fee, start, begi, tax, one-time fee
5. Y-intercept: The eagle ______.
X-intercept: the ending (usually)
Key words: finish, land, stop, limit, after
6. The eagle ______after ______.
7. What if the eagle descended at a rate of 4 feet per second? How would it change the equation?
New eqn:
8. It would change the y-intercept/x-intercept. The ______would increase/decrease by ______.
From a table
The table below shows the number of months, x, that have passed, and, y, the amount of money left in Amelia’s bank account. Use the table to answer the questions.# of Months / Total left
4 / $780
16 / $420
22 / $240
24 / $180
9. M= 10. B=
11.Eqn: / Interpret the situation:
12. Amelia started with $______and spends $______every ______.
13. What is the meaning of the slope?
She ______$______per ______.
14. What is the meaning of the y-intercept?
She ______with $______in her account.
15. What is the meaning of the x-intercept?
Amelia ______at ______.
16. What if Amelia were to increase her spending by $20 per month? How would that affect the:
a. equation: b. slope
c. y-intercept d. x-intercept?
Independent Practice
The speed limit on I-35 South is 80 during the day and 70 at night. How would the graph of the line showing the distance travelled during the nighttime differ from the graph of travel during the day?1. Day equation: y = 70x
2. Night Equation:y = 80x
3. Describethe change: The __speed_____ would increase/decrease by __10 miles_. / Jeremy is running the 1600 meter run for cross country. The race is 4 laps and he runs at a constant speed. The track is 400 meters long and runners finish the race anywhere from 5 to 10 minutes. If the y-intercept is 1600 meters and the x-intercept is 8 minutes, what is the meaning of the slope of -200?
4. Jeremey runs _200 m__ per _minutes_.
5. Eqn: y = 1600 – 200x
6. If the x-intercept were changed to 10 minutes, how would that change the situation?
He would run the race 2 minutes slower because he’s running 160 meters
7. Write the new equation: y = 1600 – 160x
The table shows how much money Amy has remaining on a gift card, b, after purchasing n coffees. Use the table for questions.
8. Review: Is this situation discrete or continuous? It is _discrete__ because __you can’t order half a cup of coffee. _____
9. What is the domain?
D: {0, 1, 2, 3, …, 9, 10}
10. What is the range?
D: {0, 2.5, 5, 7.5, …, 17.5, 20} / 11. What is the equation for this situation?
y = -2.5x + 25
12. What is the meaning of the y-intercept?
The gift card __starts with $25_
13. What is the meaning of the x-intercept?
After _10_ __coffees_ the gift card will be __empty___.
14. What is the meaning of the slope?
The __value___ increases/decreasesby __$2.50__ per __coffee___.
15. If the cost of coffee was changed so that Amy runs out of money after exactly 20 purchases, what is the new equation?
Y = 25 – 1.25x
16. Find the x- and y-intercept of the equation
x- int: (8, 0)
y – int: (0, -4) / 17. Find the y-intercept of
x- int: (7, 0)
y – int: (0, -3) / 18. Find the x- and y-intercepts of the equation
y =
x- int: (0, 0)
y – int: (0, 5)
Name: ______date: ______Period: 1 2 3 4 6 7
Exit Ticket
The graph below shows the height of an airplane as it descends into DFW. Use the graph to answer the questions below:
/ 1. What is the equation of the line?2. What is the meaning of the x-intercept?
a. The plane starts its descent at 1500 feet.
b. The plane lands at a rate of 8.3 feet per second.
c. The plane lands after 180 seconds.
d. The plane’s height is decreasing.
3. What is the meaning of the y-intercept?
a. The plane starts its descent at 1500 feet.
b. The plane lands at a rate of 8.3 feet per second.
c. The plane lands after 180 seconds.
d. The plane’s height is decreasing.
/
4. What is the meaning of the slope?
a. The plane starts its descent at 1500 feet.
b. The plane lands at a rate of 8.3 feet per second.
c. The plane lands after 180 seconds.
d. The plane’s height is decreasing.
5. Challenge! If the x-intercept is changed to 150 seconds, but the y-intercept remains constant, what is the new equation of the line?
Name: ______date: ______Period: 1 2 3 4 6 7
Exit Ticket
The graph below shows the height of an airplane as it descends into DFW. Use the graph to answer the questions below:
/ 1. What is the equation of the line?2. What is the meaning of the x-intercept?
a. The plane starts its descent at 1500 feet.
b. The plane lands at a rate of 8.3 feet per second.
c. The plane lands after 180 seconds.
d. The plane’s height is decreasing.
3. What is the meaning of the y-intercept?
a. The plane starts its descent at 1500 feet.
b. The plane lands at a rate of 8.3 feet per second.
c. The plane lands after 180 seconds.
d. The plane’s height is decreasing.
/
4. What is the meaning of the slope?
a. The plane starts its descent at 1500 feet.
b. The plane lands at a rate of 8.3 feet per second.
c. The plane lands after 180 seconds.
d. The plane’s height is decreasing.
5. Challenge! If the x-intercept is changed to 150 seconds, but the y-intercept remains constant, what is the new equation of the line?