24-25 Unit 4: 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 y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a relationship to be proportional?

Back

A proportional relationship means that two quantities maintain a constant ratio. In a graph, this relationship is represented by a straight line that passes through the origin (0,0).

Front

What is the equation of a proportional relationship?

Back

The equation of a proportional relationship can be written in the form y = kx, where k is a constant.

Front

Identify a non-proportional relationship from the following: y = 5x, y = 2.5x, y = x + 3, y = 1/2x.

Back

y = x + 3 is a non-proportional relationship because it does not pass through the origin.

Front

How do you determine if an equation represents a proportional relationship?

Back

An equation represents a proportional relationship if it can be written in the form y = kx and the graph passes through the origin.

Front

What is the slope in the equation y = 3/4x - 2?

Back

The slope in the equation y = 3/4x - 2 is 3/4.

Front

What is the y-intercept in the equation y = 3/4x - 2?

Back

The y-intercept in the equation y = 3/4x - 2 is -2.

Front

If Samantha earned $90 for working six hours, how do you calculate her hourly rate?

Back

To calculate her hourly rate, divide the total earnings by the total hours worked: $90 ÷ 6 hours = $15 per hour.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for calculating the slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What does the term 'y-intercept' refer to in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.