Question

prepare for functions
1 think about what you know about rates of change. fill in each box.
use words, numbers, and pictures. show as many ideas as you can.
what is it?
what i know about it
rate of change
examples
examples
2 circle the equation with a rate of change of 3.
$3y = 2x + 5$
$y = 6x - 3$
$y = 3x + 12$

Explanation:

Step1: Define rate of change

For linear equations in slope-intercept form $y=mx+b$, the rate of change is the slope $m$.

Step2: Rewrite first equation to slope-intercept

$$3y=2x+5 \implies y=\frac{2}{3}x+\frac{5}{3}$$
Rate of change = $\frac{2}{3}$

Step3: Identify slope of second equation

For $y=6x-3$, rate of change = $6$

Step4: Identify slope of third equation

For $y=3x+12$, rate of change = $3$

Step5: Fill in the concept map

• What Is It?: A measure of how much one quantity changes relative to another quantity; for linear relationships, it is the slope.
• What I Know About It: Can be positive (increasing), negative (decreasing), zero (constant), or undefined; calculated as $\frac{\text{change in } y}{\text{change in } x}$ for two points $(x_1,y_1)$ and $(x_2,y_2)$.
• Examples (1): Real-world: A car driving 60 miles per hour (distance changes 60 mi per 1 hr); A plant growing 2 cm per week.
• Examples (2): Mathematical: $y=2x+1$ (rate of change 2); $\frac{\Delta y}{\Delta x}=\frac{8-4}{5-3}=2$ for points (3,4) and (5,8).

Answer:

1. Concept map filled as:

• What Is It?: A measure of how one quantity changes relative to another; slope for linear relations.
• What I Know About It: Calculated as $\frac{\Delta y}{\Delta x}$; can be positive/negative/zero; describes steepness of a line.
• Examples (1): Car speed (60 mph), plant growth (2 cm/week)
• Examples (2): $y=2x+1$, $\frac{8-4}{5-3}=2$

1. The equation with a rate of change of 3 is: $y = 3x + 12$