Linear Relationships Review (Unit 3)

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: 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 starting point of the linear relationship on the y-axis.

Front

Write the equation for Marsha's earnings based on her hourly wage and starting amount.

Back

y = 15x + 20, where y is the total earnings, x is the number of hours worked.

Front

How do you set up an equation for a total cost problem involving a fixed fee and a variable cost?

Back

The equation can be set up as: Total Cost = Fixed Fee + (Variable Cost per item * Number of items). For example, for eTunes, it is: y = 7.95 + 0.95x.

Front

If Will spent $26 on eTunes, how do you find the number of songs he downloaded?

Back

Set up the equation: 26 = 7.95 + 0.95x. Solve for x to find the number of songs.

Front

What is the equation for a man descending from a height at a constant rate?

Back

y = -30x + 100, where y is the height after x minutes.

Front

How do you interpret the negative slope in the equation y = -30x + 100?

Back

The negative slope indicates that the height is decreasing as time increases, meaning the man is descending.

Front

Write the equation that represents Bob's savings over time.

Back

y = 40x + 150, where y is the total savings after x months.

Front

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

Back

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