Algebra 1: Unit 1

Rate of Change

100

I have the base equation, y=mx+b. Which variable represents rate of change?

What is m?

The variable m is known as the slope, which also stands for the rate of change.

200

A line rises 15 units and runs 5 units. What is the slope?

What is 3? 

15/5 is simplified to 3.

300

Find the slope between (-2,1) and (2,9).

What is 2?

m = 2

6-2/3-1 = 4/2, which can be simplified to 2.

400

Find the slope between (-5,1) and (-10,10).

What is -3/5?

10-1/-10-5 = 9/-15= -3/5

500

A streaming service had 120 subscribers in January. Each month, the service gained 25 new subscribers.

1. What is the rate of change?
2. Write an equation in slope-intercept form to represent the situation.
3. How many subscribers will the service have after 5 months?
4. What does the rate of change mean in this context?

what is?

1. m=25

2. y=25x+120

3. y=245

y=25(5) + 120= 245

4. The number of subscribers increases by 25 each month.

Slope Intercept Form

100

Write an equation with slope 2 and y-intercept 5.

what is y = 2x + 5?

200

Identify the slope and y-intercept of y = -3x + 4.

what is m = -3, b = 4?

300

Write the equation of a line with slope -2 and y-intercept -1.

What is y=-2x-1?

400

Explain what the y-intercept represents.

what is where the graph crosses the y-axis?

500

Graphing question: What point is always plotted first in slope-intercept form?

what is the y-intercept

Domain & Range

100

What is domain?

what is your input/all x values?

200

What is range?

what is your outputs/all y values?

300

Determine the domain of {(1,4),(2,7),(3,10)}.

what is 1,2, and 3?

400

Determine the range of {(1,7),(2,12),(3,17)}.

what is 7,12, and 17?

500

A line extends forever in both directions. How would I describe the domain?

what is set of all real numbers?

Arithmetic Sequence

100

What is the common difference of 2, 5, 8, 11...?

what is the common difference (d) is 3?

200

Explain what the common difference represents.

what is the amount added or subtracted each time?

300

In a sequence of numbers, what does a₁ represent?

what is the first term in the sequence?

400

Find the next term: -4, 1, 6, 11...

what is 16?

500

This is my sequence of numbers:

50, 45, 40, 35...

Find a₁₂ for this sequence.

what is 105?

Mixed

100

A line passes through (1, 4) and (3, 8). Find the rate of change.

what is 2?

8-4/3-1=4/2=2

200

A line has a slope of 3 and passes through (0, -2). Write the equation in slope-intercept form.

what is y=3x−2 ?

300

An arithmetic sequence begins 7, 11, 15, 19... Find the common difference and identify the a₈ for this sequence.

what is 

the common difference is d=4,

a₈=35?

400

A line has a slope of 2 and a y-intercept of 3.

Write the equation in slope-intercept form, find the value of y when x = 4, and give the rate of change.

1. y=2x+3

2. Substitute x=4

y=2(4)+3 

y=11

3. Rate of Change = 2

500

I have four ordered pairs from a graph: (1,4), (2,7), (3,10), and (4,13).

1. Find the rate of change.
2. Write the equation in slope-intercept form.
3. State the domain.
4. State the range.
5. Is this relationship continuous or discrete?

what is?

1. the rate of change is 3

2. y=3x+1

3. The domain is: 1,2,3,4

4. The range is: 4,7,10,13

5. Discrete

Because only specific points are given rather than all values between them.