Data Tables
In the Amanda coffee shop problem, she earns a bonus of this amount for opening early at 5:30am
$20
The point where both axes meet, where x = 0 and y = 0, is called this.
The origin
The second chocolate scenario — Paul takes 4 chocolates per day from a bowl of 32 — produces this type of plot.
A straight line (linear)
In the model y = b + mx, the letter b represents this part of the model.
The base (starting) value, also known as the y-intercept
The slope of a line may be calculated using this ratio
( change in y ) per ( change in x ) or " rise over run "
A rectangle has area 48 sq inches. If the length is 6 inches, the width equals this.
8 inches
In ordered pair notation (x, y), this coordinate is always listed first.
The horizontal (x) value
The first chocolate scenario — Paul takes HALF the chocolates each day — produces this type of plot.
A curve (non-linear)
Sugar Paws starts 5 meters away and runs at 2 m/s. The complete linear equation relating distance y to seconds x is this.
y = 5 + 2x
The slope of the line passing through (2, 7) and (5, 16) is this value.
( 16-7 ) / ( 5-3 ) = 9 / 3 = 3
Using the formula y = x², complete a data table for x = { 0, 1, 2, 3, 4 }
x | y = x²
--+---------
0 | 0
1 | 1
2 | 4
3 | 9
4 | 16
Jordan walks at 3 mph. After 4 hours, the ordered pair (t, d) describing his position is this.
(4, 12)
In this table: x = { 0, 1, 2, 3, 4, 5 } and y = { 5, 8, 11, 14, 17, 20 }, y increases by this amount each step.
3
At Paul's Taco Emporium: $5 base plus $2 per taco. This is the maximum number of tacos you can get for $23.
9 tacos
The slope of the line passing through (0, 10) and (4, 2) is this value.
( 2-10 ) / ( 4-0 ) = -8 / 4 =-2
Coffee prices at the Ranchos Coffee Company are going up. The price starts at $2.00 and rises 5% per year. In this year since 2015 the price first exceeds $2.50.
2020 (year 5)
In a Cartesian plane, the horizontal axis is often represented by this variable.
x
The perimeter of a square changes like this as the width increases — linear or non-linear?
Linear (P = 4w)
Amie wins a $100 gift card and spends $15 per week. The linear equation for her remaining balance y in terms of weeks x is this.
y = 100 − 15x
Jim charges $12 for 2 days and $18 for 4 days of parking. This is the per-day rate (slope).
$3 per day, i.e. ( 18-12 ) / ( 4-2 ) = 6 / 2 = 3
Rosalie's dogs eat ½ pound of food per day from a 50-lb bag. This value of t (days) corresponds to y = 0, meaning the bag is empty
t = 100 days
A plot of y = x² looks like this shape.
A curve (parabola)
The area of a square changes like this as the width increases — linear or non-linear? Explain why.
Non-linear (A = w², squaring is not a constant rate)
The units of the rate m in the model y = b + mx may be expressed as...
Units of y per unit of x, e.g., dollars per taco
A line passes through (3, 5) and (8, 20). Find the complete linear equation y = b + mx.
y = 3x − 4
m = slope = 3
b = base value = y-intercept = -4