4.1 - 4.3 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 line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

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

Back

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

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

What is the y-intercept of a linear function?

Back

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

Front

How can you identify a linear graph?

Back

A linear graph can be identified by its straight line. If the graph forms a straight line, it represents a linear function.

Front

What does the term 'm' represent in the equation y = mx + b?

Back

In the equation y = mx + b, 'm' represents the slope of the line.

Front

What does the term 'b' represent in the equation y = mx + b?

Back

In the equation y = mx + b, 'b' represents the y-intercept of the line.

Front

How do you determine if a function is linear from a set of points?

Back

To determine if a function is linear from a set of points, check if the differences in y-values divided by the differences in x-values (slopes) are constant.

Front

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

Back

The slope in real-world applications indicates how one quantity changes in relation to another, such as speed, cost per item, or growth rate.