5.1: _________________________________________________ Date: __________

Algebra 1 Advanced

Rate of Change =

Ex 1). The table shows the elevation of a hang glider over time. Is the rate of change in elevation

with respect to time constant? What does the rate of change represent?

Slope =

Ex 2). Find the slope using a graph:

a) b)

c) d)

Slope Formula:

Time

(minutes)

Elevation

(feet)

1 360

2 325

3 290

4 255

Ex 3). Find the slope using two points:

a) F(-3, 2) and G(1, 5) b) A(1, 3) and B(4, -1)

What about vertical and horizontal lines?!

Ex 4). Find the slope of each line.

a) b)

c) H(4, -3) and G(4, 2) d) X(-1, -3) and Y(5, -3)

SUMMARY:

Homework: pg. 297 #1 – 3, 8 – 22(e), 23 – 25, 26 – 34(e)

5.2: ___________________________________________________ Date: __________

Algebra 1 Advanced

Direction Variation: When the ratio of two variables is __________________.

Ex 1. Does the equation represent direction variation? If so, find the constant of variation.

a) 4y = 5x b) 2x + 3y = 6

Ex 2. Write a direct variation equation.

a) Suppose y varies directly with x and y = 40 when x = 8. What direction variation

equation relates x and y? What is the value of y when x = 12?

b) Suppose y varies directly with x and y = 10 when x = -2. What direct variation

equation relates x and y? What is the value of y when x = -15?

c) Suppose n varies directly with p and n = 9 when p = 5. What direct variation

equation relates n and p? What is the value of n when p = 8?

d) Suppose v varies directly with k and v = -6 when k = 14. What direct variation

equation relates v and k? What is the value of k when v = 8?

Ex 3. Graph a direction variation equation.

Suppose $15 (US) is worth about $150 Mexican pesos.

a) What is the equation that relates US dollars x to Mexican pesos y?

b) What is the graph of the equation in part (a)?

What do all direct variation equations have in common?

Ex 4. Writing a direct variation from a table.

For the data in the tables, does y vary directly with x? If it does, write an equation for the

direct variation.

a) b)

Homework: pg. 304 #1 – 7, 10 – 32 (e)

x y

2 5

6 15

10 25

x y

1 7

3 10

5 13

5.3 Day 1: __________________________________________ Date: __________

Algebra 1 Advanced

Slope-Intercept Form of a linear equation of a nonvertical line is:

Ex 1). Identify the slope and the y-intercept:

a) 𝑦 = 3𝑥 − 6 b) 𝑦 =1

4𝑥 + 7 c) 2𝑥 + 4𝑦 = −32

Ex 2). How would the graph of the line and the equation in Ex 1) a) change if the y-intercept was

moved down 3 units?

Ex 3). Write an equation in slope intercept form:

a) slope = 5, y-int = -8 b) slope =1

2, y-int = 3 c) slope = -6, y-int = 0

Ex 4). Write an equation from a graph:

a) b)

Ex 5). Writing an equation from two points:

Write the equation in slope-intercept form of the line that passes through the given points.

a) (1, -6) and (-3, 10) b) (3, -2) and (1, -3)

c) (-2, 9) and (1, 6) d) (-4, -1) and (-8, 7)

Homework: pg. 311 #1, 2, 4, 8 – 30 (e)

5.3 Day 2: __________________________________________ Date: __________

Algebra 1 Advanced

Slope-Intercept Form:

Using the following steps, graph all of the linear equations on the provided grid. Use the graph to

answer the questions on the back. Please make sure the lines extend the whole graph and label

each one with its corresponding letter.

STEPS TO GRAPH USING SLOPE-INTERCEPT FORM:

1. Identify the slope & y-intercept and whether your line should be increasing or decreasing

2. Start your graph by plotting the y-intercept on the y-axis (0, b).

3. a) Apply the slope from the y-intercept a few times to obtain a few more points: 𝑚 =𝑟𝑖𝑠𝑒

𝑟𝑢𝑛

3. b) It may be necessary to apply the slope backwards, so be careful that if your slope is

positive your line should be increasing; if negative, your line should be decreasing

4. Once you have at least 3 points, connect them (with a ruler) to form your line.

A. 𝒚 = 𝟐𝒙 − 𝟑 B. 𝒚 = 𝟐𝒙 + 𝟑 C. 𝒚 = 𝟐𝒙 − 𝟏 D. 𝒚 = 𝟓𝒙 − 𝟑

Slope: ___________ Slope: ___________ Slope: ___________ Slope: ___________

y-int: ___________ y-int: ___________ y-int: ___________ y-int: ___________

_________________ _________________ _________________ _________________

E. 𝒚 = 𝟏

𝟐𝒙 − 𝟓 F. 𝒚 =

𝟓

𝟐𝒙 + 𝟏 G. 𝒚 =

𝟕

𝟑𝒙 − 𝟒 H. 𝒚 = −𝟑𝒙 + 𝟔

Slope: ___________ Slope: ___________ Slope: ___________ Slope: ___________

y-int: ___________ y-int: ___________ y-int: ___________ y-int: ___________

_________________ _________________ _________________ _________________

I. 𝒚 = −𝟏

𝟑𝒙 + 𝟐 J. 𝒚 = −

𝟕

𝟐𝒙 + 𝟓 K. 𝒚 = −

𝟒

𝟑𝒙 L. 𝒚 = −

𝟓

𝟐𝒙 + 𝟑

Slope: ___________ Slope: ___________ Slope: ___________ Slope: ___________

y-int: ___________ y-int: ___________ y-int: ___________ y-int: ___________

_________________ _________________ _________________ _________________

Answer the following questions using your graphs:

1. What do graphs A, B, and C have in common?

2. Which graph is the steepest?

a) F or G?

b) D or H?

c) J or K?

d) E or G?

e) F or L?

3. What are two differences between graphs F and L?

4. What do graphs H through L have in common?

5. Explain how to move graph A to match graph C.

6. Which graph is the steepest of them all?

7. Which graph is the least steep of them all?

8. How does changing the value of b affect the graph of an equation in the form y = mx + b?

Homework: pg. 311 #3, 31 – 44, 48 – 53

5.4: ________________________________________________ Date: __________

Algebra 1 Advanced

Point-Slope Form of an equation of a nonvertical line with slope m and through point (x1, y1) is:

Ex 1). Write the equation in point-slope form:

a) m = 3; (1, -4) b) m = 1

2; (-6, -2) c) m = -5; (0, 8)

Ex 2). Graph the equations using point-slope from:

a) 𝑦 + 4 = 3(𝑥 − 1) b) 𝑦 + 7 = −2

3(𝑥 − 4)

c) 𝑦 − 3 =1

2𝑥 d) 𝑦 − 1 = −4(𝑥 − 5)

Ex 3). Write the equation of the line in point-slope form. Then transform the equation into slope-

intercept form.

a) (-2, 1) and (4, 4) b)

Ex 4). Write an equation in point-slope form given a table of values. Then transform the equation

into slope-intercept form.

a) b)

Homework: pg. 318 #1 – 5, 8 – 26 (e)

5.5: ________________________________________________ Date: __________

Algebra 1 Advanced

Standard Form of a linear equation is:

Ex 1). Find the x- and y-intercepts of the equation in standard form:

a) 2x + 6y = 18 b) 5x – 6y = 60

Ex 2). Graph the line using the intercepts:

a) 2x + 5y = 20 b) 4x - 3y = 12

What happens when A = 0? What happens when B = 0?

Ex 3). Graphing Horizontal and Vertical Lines:

a) x = 4 b) y = -3

Ex 4). Transform the equation to Standard Form:

a) 𝑦 = −3

5𝑥 + 4 b) 𝑦 − 2 ==

1

3(𝑥 + 6)

Ex 5). A festival sells ride tickets for $0.50 each and game tickets are $0.20. You have $5 to spend

on tickets at the festival. Write and graph an equation, in standard form, that describes the items

you can purchase. What are three combinations of game and ride tickets you can purchase?

Homework: pg. 325 #1 – 6, 8 – 36(e)

5.6: _________________________________________________ Date: __________

Algebra 1 Advanced

Parallel Lines:

Ex 1). Write an equation of a parallel line, in slope-intercept form:

a) passes through (2, 15) and parallel to y = 4x – 1

b) passes through (-3, -1) and parallel to y = 2x + 3

Perpendicular Lines:

Ex 2). Classify Lines:

Are the graphs parallel, perpendicular, or neither?

a) 2𝑦 = −3𝑥 + 6 𝑎𝑛𝑑 𝑦 =2

3𝑥 + 2 b) 𝑦 =

3

4𝑥 + 7 𝑎𝑛𝑑 4𝑥 − 3𝑦 = 9

Ex 3). Write an equation of a perpendicular line, in slope-intercept form:

a) passes through (10, 15) and is perpendicular to 𝑦 = −5

6𝑥 − 2

b) passes through (1, 8) and is perpendicular to 𝑦 = 2𝑥 + 1

Homework: pg. 333 #1 – 5, 8 – 24 (e), 27 – 30

5.7: _________________________________________________ Date: __________

Algebra 1 Advanced

A ___________ _______ is a graph that relates two different sets of data by displaying data as

ordered pairs.

You can use scatter plots to find ___________ in data.

Two sets of data may have one of the three following types of relationships:

Ex 1). The table shows the amount of time spent studying for a final exam by 8 students and the

grades that they earned.

Study Time vs. Grade

Study Time

(hours)

Grade

Earned

7 88

3 79

5 92

1 71

0 62

6 94

4 82

2 65

a) Make a scatter plot of the data.

b) What type of relationship does the scatter plot show?

When two sets of data have a positive or negative correlation, you can use a __________ _______

to show the correlation more clearly.

A trend line is a line on a scatter plot, drawn _______ the points, that shows a correlation.

______________________ is estimating a value between two known values.

______________________ is predicting a value outside the range of unknown values.

Ex 2). Make a scatter plot of the data below. Draw a trend line and write its equation. Use the

equation to estimate the deer population in the 12th year of the study.

Deer Population Study

Year Population

1 1260

2 1375

3 1310

4 1490

5 1625

6 1680

7 1740

8 1715

The trend line that shows the relationship between two sets of data most accurately is called the

_______ ____ _______ ______.

________________ is when a change in one quantity causes a change in a second quantity. A

correlation between quantities does not always imply causation.

Ex 3). In the following situations, is there likely to be a correlation? If so, does the correlation

reflect a causal relationship? Explain.

a) The height of a student and the grade earned on a quiz.

b) The price of bananas at a grocery store and the number of pounds of bananas bought.

Homework: pg. 340 #1 – 4, 7 – 10, 19, 20

5.8: ________________________________________________ Date: __________

Algebra 1 Advanced

An absolute value function has a _____________ graph that opens up or down. The parent

function for the family of absolute value functions is __________.

A _______________ is a shift of a graph horizontally, vertically, or both. The result is a graph of the

same ________ and _________, but in a different position.

Ex 1). Below are the graphs of 𝑦 = |𝑥| and 𝑦 = |𝑥| − 4. How are the graphs related?

VERTICAL TRANSLATIONS:

𝑦 = |𝑥| + 𝑘 translates the graph of 𝑦 = |𝑥| _______ k units.

𝑦 = |𝑥| − 𝑘 translate the graph of 𝑦 = |𝑥| __________ k units.

Ex 2). What is the graph of 𝑦 = |𝑥| + 2? Ex 3). What is the graph of 𝑦 = |𝑥| − 1?

HORIZONTAL TRANSLATIONS:

𝑦 = |𝑥 + ℎ| translates the graph of 𝑦 = |𝑥| __________ h units.

𝑦 = |𝑥 − ℎ| translates the graph of 𝑦 = |𝑥| ___________ h units.

Ex 4). What is the graph of 𝑦 = |𝑥 + 4|? Ex 5). What is the graph of 𝑦 = |𝑥 − 3|?

Ex 6). At the right is the graph of 𝑦 = −|𝑥|. Graph each function by translating 𝑦 = −|𝑥|.

a) 𝑦 = −|𝑥| − 1 b) 𝑦 = −|𝑥 + 3|

Homework: pg. 348 #1 – 4, 6 – 28(e), 34