Comparing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

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

Back

The y-intercept of a linear equation can be found by setting x to 0 in the equation and solving for y.

Front

What is the y-intercept of the equation y = 2x + 3?

Back

The y-intercept is 3, which is the value of y when x = 0.

Front

How do you compare the slopes of two linear functions?

Back

To compare the slopes, look at the coefficients of x in the equations. The larger the coefficient, the steeper the slope.

Front

What is the slope of the equation y = 3x - 3?

Back

The slope is 3, which means for every 1 unit increase in x, y increases by 3 units.

Front

If two linear functions have the same slope, what does that imply about their graphs?

Back

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

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, indicating the value of y when x is 0.

Front

How can you determine which linear function has a greater y-intercept?

Back

Compare the constant term (b) in the equation y = mx + b. The function with the larger b value has a greater y-intercept.

Front

What is the y-intercept of the equation y = 1/2x + 1?

Back

The y-intercept is 1, which is the value of y when x = 0.