Definitions
Tables, Graphs, & Equations
Transformations
Slopes & Intercepts
Critiquing and Justifying
100
This is the geometric transformation where you flip something over a line.
What is a reflection?
100
In the equation below, what is the slope and what is the y-intercept?
y = 2x + -3
The slope is 2 and the y-intercept is -3.
100
Describe the rotation that is shown below. What is the center of rotation, the angle of rotation, and the direction of the rotation?
Center of rotation: point A
Angle of rotation: 90 degrees
Direction: counterclockwise
100
This is the place where a line intercepts the y-axis.
What is a y-intercept?
100
Julia says that the two triangles below are congruent. Why is she incorrect?
When two triangles are congruent, the corresponding angles and corresponding sides are equal. In this example, the corresponding sides are proportional. These two triangles are similar but not congruent.
200
Every equation of a line has a general form that looks like this...
What is "y = mx + b" ?
200
Write an equation to represent the relationship shown in the table below.
What is y = 3x - 1
200
Below, triangle ABC is dilated around the origin to form triangle A'B'C'. What is the scale factor for the dilation?
The scale factor is 2.
200
Find the slope in the graph below.
The slope is 2 or 2/1.
200
Are the two triangles below congruent or similar? Why?
They are congruent because the corresponding sides and angles are equal.
300
This is the formula to find the slope of a line.
What is
a) rise over run; or
b) the change in the y-values divided by the change in the x-values; or
c) the vertical distance divided by the horizontal distance
300
Write an equation to represent the line in the graph below.
What is "y = 2x + 4?"
300
Write a rule that translates IRT, which is the figure in blue, onto I'R'T, which is the figure in red.
(x, y) ----> (x + 6 , y - 4)
300
Find the slope in the table below.
The slope is 2.
300
Why does the table below show a linear relationship between variables?
It shows a linear relationship because y changes by a constant amount every time x changes by 1. Specifically, y changes by 4 every time x changes by 1.
400
A proportional relationship between variables.
In a proportional relationship every x-value can be multiplied by a constant number to get the corresponding y-value.
400
Below is a graph illustrating Angela's hiking elevation at different times. Describe the situation. At what elevation does Angela start? What happens over time? What happens at the end?
Angela starts at an elevation of 360 feet and her elevation decreases at a rate of 20 feet per minute. In 18 minutes, she is at an elevation of 0 feet or sea level.
400
If you reflected the figure below over the line y = x, what will the coordinates of A' be?
(2, -2)
400
What is the slope in the graph below, and what does it mean in this situation?
The slope is -1/25 or -.04. You could say that it means that the gasoline in the tank decreases by 1 gallon every time 25 miles is driven, or you could say that the gasoline decreases by 1/25 or .04 gallons every time 1 mile is driven.
400
Janice says that the slope of the line below is 3/4. Why is that incorrect?
3/4 is incorrect because you go DOWN 3 and then to the right 4, so the slope is -3/4.
500
A linear relationship between variables
This is a relationship between variables where the y-values change by a constant amount every time the x-values change by 1.
500
Alondra wants to hire a company to install a fence. They tell her that it will cost $300 to install 10 feet of fencing, and $450 to install 20 feet of fencing. The company charges a one-time cost and a cost per foot of fencing. Write an equation to represent the cost, "y," of installing "x" feet of fencing, and tell us the one-time cost and cost per foot.
y = 150 + 15x
The one-time cost is $150 and the cost per foot is $15.
500
If DEFG below is dilated around the origin by a scale factor of 1/2, what will be the coordinates of the new figure?
D': (.5, 1.5)
E': (2.5, 1.5)
F': (3.5, -.5)
G': (.5, -.5)
500
Find the slope of the line below. Make sure to show your work.
The slope is undefined.
Work: change in y/ change in x = 6/0 = undefined.
500
Describe how downloads changed over the years shown.
In 2011, about 35% of total music sales were through downloads. That increased to a little above 40% by 2014, then decreased steadily to about 30% by 2018.