Linear Relationships

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be expressed in the form of an equation, typically written as 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 much y changes for a one-unit increase in x.

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 represents the point where the line crosses the y-axis.

Front

How do you write an equation for a linear relationship?

Back

An equation for a linear relationship can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

If Billy spends $15 each week from his $200, what is the equation representing his balance over time?

Back

The equation is y = -15x + 200, where y is the balance and x is the number of weeks.

Front

What is the relationship between the number of portraits sold (y) and the number of months (x) if Beth sells 3 portraits per month?

Back

The relationship can be represented by the equation y = 3x, where y is the number of portraits sold and x is the number of months.

Front

How do you determine the total cost at a dance if it costs $5 to enter and $0.75 for each snack?

Back

The total cost can be represented by the equation y = 0.75x + 5, where y is the total cost and x is the number of snacks purchased.

Front

If Sonia has $40 and spends $2 each day for lunch, what is the equation for her lunch account balance?

Back

The equation is y = -2x + 40, where y is the balance and x is the number of days.

Front

What does a negative slope indicate in a linear relationship?

Back

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

Front

What does a positive slope indicate in a linear relationship?

Back

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