The manager of a furniture factory finds that it costs 2200...

The manager of a furniture factory finds that it costs $\$ 2200$ to produce 100 chairs in one day and $\$ 4800$ to produce 300 chairs in one day. a. Assuming that the relationship between cost and the number of chairs produced is linear, find a linear function $C$ that models the cost of producing $x$ chairs in one day. b. Draw a graph of $C$. What is the slope of this line? c. At what rate does the factory's cost increase for every additional chair produced?

The manager of a furniture factory finds that it costs $\$ 2200$ to produce 100 chairs in one day and $\$ 4800$ to produce 300 chairs in one day.
a. Assuming that the relationship between cost and the number of chairs produced is linear, find a linear function $C$ that models the cost of producing $x$ chairs in one day.
b. Draw a graph of $C$. What is the slope of this line?
c. At what rate does the factory's cost increase for every additional chair produced?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Graphing Linear Equations

Graphing linear equations involves plotting the y-intercept and using the slope to determine the line's direction and steepness. This visual representation is essential for understanding the relationship between the variables and for making predictions based on the linear model.

Y-Intercept

The y-intercept is the point where the line crosses the y-axis. It indicates the value of the dependent variable when the independent variable is zero, often representing a fixed starting cost or initial condition before any changes occur.

Slope (Rate of Change)

The slope of a linear function represents the constant rate at which the dependent variable changes when the independent variable increases. It quantifies how much the dependent variable, such as cost, increases or decreases per unit change in the independent variable.

Linear Function

A linear function describes a relationship between two variables with a constant rate of change, producing a straight-line graph. This concept is foundational in mathematics and is used to model real-world situations where one quantity changes at a constant rate with respect to another.

Transcript

Please give Ace some feedback