Bell Ringer Dec. 2-6: Writing Equations

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope in a linear equation represent?

Back

The slope 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 is the y-intercept in a linear equation?

Back

The y-intercept 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 total cost that includes a fixed fee and a variable cost?

Back

The equation is written as y = mx + b, where m is the variable cost per unit, x is the number of units, and b is the fixed fee.

Front

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

Back

y = 3x + 2.

Front

What is the equation for the total cost of renting a car for x days if the daily rate is $40 and there is a $15 insurance fee?

Back

y = 40x + 15.

Front

How do you represent a decrease in height over time in a linear equation?

Back

You can represent it as y = initial height - rate of descent * time, e.g., y = 100 - 30x.

Front

What is the equation for the total cost of a holiday meal for x people if it costs $12.50 per person plus a $30 delivery fee?

Back

y = 30 + 12.50x.

Front

What does it mean if a linear equation has a negative slope?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.