Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane 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 y-value with respect to the x-value. It indicates how steep the line is and the direction it goes (positive or negative).

Front

How do you find the slope from 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. It is represented by the value of b in the equation y = mx + b.

Front

Given the equation y = 3/2x + 3, what is the slope?

Back

The slope is 3/2.

Front

Given the equation y = 3/2x + 3, what is the y-intercept?

Back

The y-intercept is (0, 3).

Front

What is the equation of a horizontal line?

Back

The equation of a horizontal line is of the form y = b, where b is a constant.

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is of the form x = a, where a is a constant.

Front

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

Back

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

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal.