Download Algebra 2 Pre AP PS: More Linear Function Fun a) On the graph

Algebra 2 Pre AP
PS: More Linear Function Fun
1.
a) On the graph above, draw and write the equation of the line that goes through the point (6,1.891) and
(0, 1.033) in point slope form. This is the regression or trendline and you will use this equation for the
remainder of the questions)
b) What does the x variable, y variable, and slope of the line in part a represent in the context of this situation?
c) According to the equation, how much will gasoline cost in 2020 rounded to the nearest cent?
2. For the function f(x), f(5)=9 and f(10)=-6.
a) What is the equation for the function of f(x) in slope intercept form?
b) Find f
-1
(x)
c. Find f(1), f(100), f
-1
(-15)
3. Read the information below about several lines. If there is enough information to raw a graph and find the
equation, write ‘enough information’ and fine the equation. If there is not enough information, tell what you
would need to find an equation.
a. Line A has a slope of 2
b. Line B is horizontal and goes through the point (2,2)
c. Line C passes through the origin and has a slope of -1.
d. Line D is parallel to the line y=4x-5 and passes through the point (0,6)
e. Line E passes through the point (-2,8) and (3,-11)
f. :one F passes through the point (-4,8)
4. The manager of a restaurant found that the cost of producing 100 cups of coffee is $11.12, while the cost of
producing 400 cups is $41.12. Assume the cost function is linear. Define your variables. Indicate which are
independent and dependent.
a. Write a function in point slope form rounding your slope to the nearest cent,
b. What is the cost per cup?
c. What is cost of producing no cups of coffee?
d. Find the total cost of producing 1000 cups.
e. If the restaurant spent $200 producing cups of coffee in one week, how many cups of coffee did it sell? Round
to the nearest whole cup
5. Find the value of k if a line with a slope of 3/8 passes through the points (-1,4) and (k,-3)
6. Write, in point-slope form, the equation of the perpendicular bisector of the line that goes through (3,-5) and
(7,1). Perpendicular bisector is a line that is perpendicular and goes through the midpoint of the given line.
7. Harper, Elie, and Raina are having a skateboard race. Haper began at the starting line and rode at a constant rate of 3 feet
per second. Elie got a 5ft head start and rode 2ft every 3 seconds. Raina rode 3 feet every 5 seconds and had a 2ft. head
start.
a. Write an equation for each line.
b. After how many seconds did Harper catch up to Elie? How far were they from the starting line?
c. If the race is 9 feet long, who won?
d. Will Raina ever catch up to Elie? How do you know?
8. Graph the following lines on the grid below and label
a. Line A: y=-2x+4
b. Line B:5x-3y=15
c. Line C: Parallel to the line 6x+2y=9, and goes through the point (2,-3)
d. Line D: Perpendicular to the line y= -1/3(x+3)-2 and goes through the point (3,-1)
Needs one point
Harper: y=3x
Elie: y=2/3x+5
Raina y=3/5x+2
Needs the slope
or a second point.
21, -276, 13
The change in cost Enough
of a gallon of
information, Y=2
gasoline in
September per
year
Enough
information
y=4x+6
Y=0.143x+1.033
Y=-1/3x+8
NO,
Harper
The average price
for a gallon of
gasoline
Y=
0.10(x-400)+41.12
$4.18
Y=-3x+24
$0.10
$1.12
About 2.1 seconds
and 6.4 feet.
$101.12
Enough
information, y= -x
Enough
information y=3.8x-0.4
1989
The number of
years after 1998