Writing Linear Equations from Verbal Descriptions POL

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What does the y-intercept (b) represent in a linear equation?

Back

The y-intercept (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you write a linear equation from a verbal description?

Back

Identify the fixed costs and variable costs from the description, then express the total cost as a function of the variable.

Front

If a cookie costs $3 and there is a $2 boxing fee, what is the expression for the total cost of x cookies?

Back

Total cost = 3x + 2.

Front

What is the equation for a cell phone bill that has a monthly fee and a per-minute charge?

Back

C = 15 + 0.20x, where C is the total bill and x is the number of minutes used.

Front

What does the equation y = -25x + 120 represent in a real-world context?

Back

It represents a situation where there are 120 gallons of water in a tank, and it releases water at a rate of 25 gallons per minute.

Front

How do you represent the cost of a holiday meal for x people with a per-person cost and a delivery fee?

Back

y = 30 + 12.50x, where y is the total cost.

Front

If Lisa bought shirts that were 3 more than twice the number of pants, how is this represented?

Back

s = 3 + 2p, where s is the number of shirts and p is the number of pants.

Front

What is the difference between fixed costs and variable costs?

Back

Fixed costs do not change with the level of output (e.g., delivery fees), while variable costs change with the level of output (e.g., cost per cookie).