Comparing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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 the y-value changes for a unit change in the x-value.

Front

How do you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test on its graph.

Front

What is the slope-intercept form of a linear equation?

Back

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

Front

How can you compare the slopes of two linear equations?

Back

To compare the slopes of two linear equations, identify the coefficients of x in their equations. The equation with the larger coefficient has the greater slope.

Front

What does it mean if two linear equations have the same slope?

Back

If two linear equations have the same slope, they are parallel lines and will never intersect, meaning they have no points in common.

Front

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

Back

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

Front

How do you find the slope between two points on a line?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the graphical representation of a linear function?

Back

The graphical representation of a linear function is a straight line on a coordinate plane.

Front

What is the difference between a function and a non-function?

Back

A function has a unique output for every input, while a non-function may have multiple outputs for a single input.