Word problem wizards
A gym charges a $50 joining fee and $20 per month. What is the y-intercept in this scenario?
$50
Find the next number in the sequence: 2,5,8,11...
14
Does the equation y=x2+1 represent a linear or non-linear function?
Non-linear
In the equation y=4x−2, which number represents the slope?
4
Where does a line cross the y-axis if the equation is y=2x+7?
At 7 or (0,7)
You start with 100 songs on your phone and download 5 new songs every week. Write an equation for the total songs (y) after x weeks.
y=5x+100
What is the "common difference" in the sequence: 20,15,10,5...
-5
Describe the visual difference between a linear and non-linear graph.
Linear is a straight line; non-linear is curved or broken
What is the slope of a horizontal line?
Zero
What is the y-coordinate of the y-intercept for any proportional relationship?
0
A candle is 12 inches tall and burns at a rate of 1.5 inches per hour. Is the slope of this relationship positive or negative?
Negative, because the height is decreasing
If the first term is 10 and the common difference is 4, what is the 3rd term?
18
In a table, if the x-values increase by 1 and the y-values increase by 3 every single time, is it linear?
Yes, it has a constant rate of change
300: If a line passes through (0,0) and (2,10), what is the rate of change?
5
A taxi charges $5 just to get in, plus $2 per mile. Which value is the y-intercept?
$5
A plumber charges a flat fee plus an hourly rate. If 2 hours cost $150 and 3 hours cost $200, what is the plumber's hourly rate?
$50 per hour
Write an equation in y=mx+b form for the sequence 5,7,9,11...
( y=2x+3 )
Does the equation y=x4 represent a linear function?
No, because the variable is in the denominator
Find the slope between the points (1,5) and (3,11).
3
If a table shows (2,10) and (3,13) with a constant rate of change, what is the y-value when x=0?
4
A hiker starts at an elevation of 2,000 feet and descends to sea level (0 feet) in 4 hours at a constant rate. What is the hiker’s rate of change?
−500 feet per hour
In a sequence, if a1=12 and the pattern is "subtract 3," what is the 10th term?
-15
Given a pattern of squares where the side length doubles each time, is the relationship between side length and area linear or non-linear?
Non-linear; area grows quadratically
How do you find the slope of a line from a table if the x-values are not counting by 1s?
Use the formula y2-y1/x2-x1
Look at a graph where the line crosses the vertical axis at −3. Write the end of the equation (y=mx+?)
-3