Comparing 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, typically described by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope represent in a linear equation?

Back

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

Back

The y-intercept is the value of y when x is 0. It represents the point where the line crosses the y-axis.

Front

How do you identify the slope from a linear equation in the form y = mx + b?

Back

The slope is the coefficient of x (m) in the equation.

Front

What does it mean if the slope of a line is positive?

Back

A positive slope indicates that as the value of x increases, the value of y also increases.

Front

What does it mean if the slope of a line is negative?

Back

A negative slope indicates that as the value of x increases, the value of y decreases.

Front

In the equation y = 25x, what does the number 25 represent?

Back

The number 25 represents the slope of the line, indicating that for every increase of 1 in x, y increases by 25.

Front

What is the significance of the y-intercept in real-world scenarios?

Back

The y-intercept often represents a starting value or initial condition in real-world scenarios, such as a fixed cost before any variable costs are added.

Front

How can you determine the y-intercept from a graph?

Back

The y-intercept can be determined by finding the point where the line crosses the y-axis.

Front

What is the equation of a line with a slope of 3 and a y-intercept of 4?

Back

The equation of the line is y = 3x + 4.