Graphing Linear Functions (Flashcard)

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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.

Front

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

Back

The slope (m) is 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

If a line has a slope of 1, what does this mean?

Back

A slope of 1 means that for every unit increase in x, y increases by the same amount. The line rises at a 45-degree angle.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as x increases, y decreases. The line falls from left to right.

Front

What is the slope of the line represented by the equation y = -2x + 5?

Back

The slope of the line is -2.

Front

How do you plot the point (3, 4) on a graph?

Back

To plot the point (3, 4), move 3 units to the right on the x-axis and 4 units up on the y-axis.

Front

What is the relationship between the slope and the steepness of a line?

Back

The greater the absolute value of the slope, the steeper the line. A slope of 0 indicates a horizontal line.

Front

What does it mean if a line has a slope of 0?

Back

A slope of 0 means the line is horizontal and does not rise or fall as x changes.