Comparing Linear Functions

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise/run).

Front

How do you determine the rate of change from a linear function?

Back

The rate of change is represented by the slope of the function. In the equation y = mx + b, 'm' is the slope.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

Front

What is the difference between initial fee and additional fee in a cost function?

Back

The initial fee is a fixed cost that does not change with the number of guests, while the additional fee varies based on the number of guests.

Front

How can you compare the rates of change of two linear functions?

Back

You can compare the slopes of the functions; the function with the greater slope has a greater rate of change.

Front

What is the equation of a line in slope-intercept form?

Back

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

Front

What does it mean if two functions have the same rate of change?

Back

If two functions have the same rate of change, they are parallel lines and will never intersect.

Front

How do you find the slope from a table of values?

Back

To find the slope from a table, select two points (x1, y1) and (x2, y2) and use the formula (y2 - y1) / (x2 - x1).

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, indicating the value of y when x is 0.

Front

How can you represent a linear function graphically?

Back

A linear function can be represented graphically as a straight line on a coordinate plane.