Comparing Functions

Front

What is a y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b, where b is the y-intercept.

Front

How do you determine which linear equation has a higher y-intercept?

Back

Compare the constant term (b) in the slope-intercept form (y = mx + b) of each equation. The equation with the larger b value has the higher y-intercept.

Front

What does the slope of a linear equation represent?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is. It is calculated as the change in y divided by the change in x.

Front

How can you identify which linear equation has a steeper slope?

Back

Compare the slope values (m) in the equations. The equation with the larger absolute value of m has the steeper slope.

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.

Front

What is the difference between a positive and negative slope?

Back

A positive slope indicates that as x increases, y also increases, while a negative slope indicates that as x increases, y decreases.

Front

What does it mean for a function to have a greater rate of change?

Back

A greater rate of change means that for a given change in x, the change in y is larger compared to another function.

Front

How do you calculate the rate of change between two points on a graph?

Back

The rate of change is calculated using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the two points.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent various real-world rates, such as speed, growth rate, or efficiency, depending on the context of the problem.

Front

How can you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept, plot it on the graph, and use the slope to find another point, then draw a line through the points.