Question

todays review opportunity
identify the initial value and rate of change of a linear function given a graph or table.

x	0	1	2	3
y	1	3	5	7

initial value = 0
rate of change = 2
write an equation for a linear function.
y = 2x + 1
you will use these skills in todays lesson. would you like to practice identifying the rate of change and initial value and writing a linear function?
yes no

Explanation:

Step1: Find the initial value

The initial value of a linear function is the \(y\) - value when \(x = 0\). Looking at the table, when \(x=0\), \(y = 1\).

Step2: Calculate the rate of change

The rate of change (slope \(m\)) of a linear function is given by the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points \((x_1,y_1)=(0,1)\) and \((x_2,y_2)=(1,3)\). Then \(m=\frac{3 - 1}{1-0}=\frac{2}{1}=2\).

Step3: Write the equation of the linear function

The slope - intercept form of a linear function is \(y=mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. We found \(m = 2\) and \(b=1\), so the equation is \(y=2x + 1\).

Answer:

Initial value \(=1\), rate of change \(=2\), equation \(y = 2x+1\)