P-K Real World Problems w/ Linear Equations

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 an equation for a real-world problem involving costs?

Back

Identify the fixed costs and variable costs, then use the equation format y = mx + b, where y is the total cost, m is the variable cost per unit, x is the number of units, and b is the fixed cost.

Front

In the equation y = 30x + 20, what do the numbers 30 and 20 represent?

Back

In this equation, 30 represents the cost per hour of renting a canoe (the slope), and 20 represents the initial transportation fee (the y-intercept).

Front

What is the independent variable in a linear equation?

Back

The independent variable is the variable that is changed or controlled in an experiment or equation, often represented by x.

Front

What is the dependent variable in a linear equation?

Back

The dependent variable is the variable that is measured or affected in an experiment or equation, often represented by y.

Front

How do you determine the total cost of renting a canoe for x hours?

Back

Use the equation y = 30x + 20, where y is the total cost, 30 is the hourly rate, and 20 is the transportation fee.

Front

If Joanna starts with $10 and earns $20 each week, how much will she have after 3 weeks?

Back

After 3 weeks, Joanna will have $10 + (3 weeks * $20/week) = $10 + $60 = $70.

Front

What is the equation for the total cost of x pounds of fruit if Lee charges $3 for a basket and $2.50 per pound?

Back

The equation is y = 2.50x + 3, where y is the total cost, 2.50 is the cost per pound, and 3 is the cost of the basket.