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Quarter 2 Assessment Review
Algebra 1
Semester 1 Final
QUESTION 1: Four points on a line are shown in the table below. What is the slope of this line?
x y
1 0
3 -1
5 -2
7 -3
(1,0)
(3,-1)
(5,-2)
(7,-3)
Pick 2 points, and calculate slope using formula:
(x, y)
ANSWER 1: Four points on a line are shown in the table below. What is the slope of this line?
Let’s take the first 2 points:
x y
1 0
3 -1
5 -2
7 -3
(1,0)
(3,-1)
0 – -1
1 – 3
1
-2
*Note: The slope is the same between any two points on a line. So it does not matter which two points you choose
1
2
m = ---------
m = --------- - ---
QUESTION 2: The table from Question 1 represents a linear function. Why is this function linear?
First, we need to know…
What is a function? What does it mean
for a function to be linear?
x y
1 0
3 -1
5 -2
7 -3
ANSWER 2: The table from Question 1 represents a linear function. Why is this function linear?
FUNCTION: For each x value there is exactly one y value.
One way to remember:
x y
1 0
3 -1
5 -2
7 -3
x y
1 0
3 -1
3 -2
7 -3
xBoyfriend
yGirlfriend
John Amy
Tony Maria
Tony Susie
Dan Trish
FunctionNOT a Function
ANSWER 2: The table from Question 1 represents a linear function. Why is this function linear?
LINEAR: A linear relationship has a graph that’s a straight line.
A straight line has a constant rate of change (slope).
SO..The function is linear because:
It has a constant rate of change (or slope)
Slope = -------------------- = -------------
= ---------
x y
1 0
3 -1
5 -2
7 -3
change in y
change in x
+2
+2
+2
-1
-1
-1
-1+2
rise
run
In WORDS:
The y-values decrease by 1 as the x-values increase by 2.
QUESTION 3: A growing L-Pattern made of small square tiles is shown below. What equation represents the total number of tiles, T, in terms of the figure number, n?
Figure 1 Figure 2 Figure 3
ANSWER 3: A growing L-Pattern made of small square tiles is shown below. What equation represents the total number of tiles, T, in terms of the figure number, n?
Figure 1 Figure 2 Figure 3
1. What is the constant rate of change in the pattern?
Total tiles: 5
Total tiles: 8
Total tiles: 11+3
+3
T = 3n
ANSWER 3: A growing L-Pattern made of small square tiles is shown below. What equation represents the total number of tiles, T, in terms of the figure number, n?
How can we represent this pattern in a table?
Figure number
n
Total number of tiles
T
1 5
2 8
3 11
x y Rate of change = -------------------- change in y
change in x
= --------------------
change in T
change in n
+3
+3
+1
+1
= ------------+3
+1
= 3
3 is the slope of this equation
ANSWER 3: A growing L-Pattern made of small square tiles is shown below. What equation represents the total number of tiles, T, in terms of the figure number, n?
Figure 1 Figure 2 Figure 3
Total tiles: 5
Total tiles: 8
Total tiles: 11
3(2) = 6
3(1) = 3
so far we have… T = 3n
3(3) = 9
1. What is the remaining number of tiles we need to add to get the total number of tiles?
T = 3n + 2
+2 = 5
+2 = 8
+2 = 11
ANSWER 3: A growing L-Pattern made of small square tiles is shown below. What equation represents the total number of tiles, T, in terms of the figure number, n?
Figure 0 Figure 1 Figure 2 Figure 3
Total tiles: 5Total tiles: 8
Total tiles:11
3(2) + 2 = 8
3(1) +2 = 5
3(3) + 2 = 11
3(0) +2 = 2
Can you guess what Figure 0 would look like?
Total tiles: 2
QUESTION 4: Kelvyn Park’s volleyball team sells candy bars as a fundraiser. The table below shows the total weight of a box with 1, 2, 3, and 4 candy bars. Write an algebraic rule (equation) that can be used to determine the total weight of the box for any number of candy bars.
Number of candy bars in
box
Total weight (ounces)
1 7
2 12
3 17
4 22
ANSWER 4: Kelvyn Park’s volleyball team sells candy bars as a fundraiser. The table below shows the total weight of a box with 1, 2, 3, and 4 candy bars. Write an algebraic rule (equation) that can be used to determine the total weight of the box for any number of candy bars.
Number of candy bars
in box
x
Total weight (ounces)
y
1 7
2 12
3 17
4 22
y = Total weight
x = Any number of candy bars
1. What is the rate of change (slope)?
Rate of change = -------------------- change in y
change in x
+5
+5
+5
+1
+1
+1
= ----------+5
+1= 5
So far, we know: y = 5x ____
y = mx + b
ANSWER 4: Kelvyn Park’s volleyball team sells candy bars as a fundraiser. The table below shows the total weight of a box with 1, 2, 3, and 4 candy bars. Write an algebraic rule (equation) that can be used to determine the total weight of the box for any number of candy bars.
Number of candy bars
in box
x
Total weight (ounces)
y
1 7
2 12
3 17
4 22
y = 5x ____
5( ) = 5
5( ) = 10
5( ) = 15
5( ) = 20
2. What must we add or subtract to 5x to get the y value in the table?
y = 5x + 2+2 =
+2 =
+2 =
+2 =
ANSWER 4: Kelvyn Park’s volleyball team sells candy bars as a fundraiser. The table below shows the total weight of a box with 1, 2, 3, and 4 candy bars. Write an algebraic rule (equation) that can be used to determine the total weight of the box for any number of candy bars.
Let’s break this down.. What does each number and variable
represent in this algebraic rule?
y = 5x + 2
Total weightNumber of candy bars
Rate of change
Weight of box
