Comparing Functions

Front

What is a y-intercept in a linear function?

Back

The y-intercept is the point where the graph of a function intersects the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How do you determine the slope of a linear equation?

Back

The slope of a linear equation in the form y = mx + b is represented by 'm', which indicates the rate of change of y with respect to x.

Front

What does a steeper slope indicate about a linear function?

Back

A steeper slope indicates a greater rate of change; the larger the absolute value of the slope, the steeper the line.

Front

How can you compare the y-intercepts of two linear equations?

Back

To compare y-intercepts, evaluate the constant term (b) in the equations y = mx + b; the larger the b value, the higher the y-intercept.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

If two equations have the same slope, what can be said about their graphs?

Back

If two equations have the same slope, their graphs are parallel and will never intersect.

Front

What does it mean if two linear equations have the same y-intercept?

Back

If two linear equations have the same y-intercept, their graphs intersect at the y-axis, but they may have different slopes.

Front

How do you find the y-intercept from a linear equation?

Back

To find the y-intercept from a linear equation in the form y = mx + b, set x to 0 and solve for y, which will give you the value of b.

Front

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

Back

The slope can represent rates of change in real-world contexts, such as speed, cost per item, or growth rates.

Front

How can you tell which of two linear equations has a greater y-intercept?

Back

Compare the constant terms (b) in the equations; the equation with the larger b value has the greater y-intercept.