Task Sets: Construct a function to model a linear relationship between two quantities - Common Core Math - Grade 8

Recall / Warm-Up

In the equation $y = mx + b$ , which part tells you the rate of change (how much $y$ changes for each $1$ -unit increase in $x$ )?

$m$

$b$

$x$

$y$

Find the slope between the points $(2, 7)$ and $(5, 16)$ using $m = \dfrac{y_2 - y_1}{x_2 - x_1}$ .

A table includes the row $x = 0, y = 12$ . For a linear function, what is the initial value $b$ ?

$b = 0$

$b = 12$

You cannot tell without the slope

$b = 12x$

Fluency Practice

A bike shop charges a $20$ -dollar flat fee plus $4$ dollars per hour to rent a bike. Which equation models the total cost $y$ in dollars for $x$ hours?

$y = 4x + 20$

$y = 20x + 4$

$y = 24x$

$y = 4x - 20$

A linear function passes through $(0, 9)$ and $(4, 21)$ . Find each value, then write the model. Rate of change $m = $ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ . Initial value $b = $ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .

rate of change m:

initial value b:

A linear function has slope $m = 5$ and passes through the point $(2, 16)$ . Use $b = y - mx$ to find the initial value $b$ .

A linear function passes through $(2, 10)$ and $(6, 26)$ . What is the rate of change $m$ ?

Exercises: Building Linear Models from Data and Context

Recall / Warm-Up

Fluency Practice