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 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

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 do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form y = mx + b.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as the value of x increases, the value of y also increases, resulting in an upward slant of the line.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the value of x increases, the value of y decreases, resulting in a downward slant of the line.

Front

What is the formula for calculating the rate of change?

Back

The rate of change is calculated using the formula m = (change in y) / (change in x), which is the same as the slope.

Front

How can you identify the x-intercept of a linear function?

Back

The x-intercept is the point where the line crosses the x-axis, found by setting y = 0 in the equation and solving for x.

Front

What is the significance of the coefficients in the equation of a line?

Back

In the equation y = mx + b, m represents the slope and b represents the y-intercept, both of which are crucial for graphing the line.