Linear Functions Review

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 in 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 equation y = mx + b.

Front

If a line has a slope of 3, what does this mean?

Back

A slope of 3 means that for every 1 unit increase in x, the value of y increases by 3 units.

Front

What is the difference between positive and negative slopes?

Back

A positive slope indicates that the line rises as it moves from left to right, while a negative slope indicates that the line falls as it moves from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, meaning there is no change in the y-value as the x-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is 0, leading to division by zero in the slope formula.

Front

How can you determine which of two lines has a greater slope?

Back

Compare the slope values (m) of the two lines. The line with the larger absolute value of m has a greater slope.

Front

What does it mean if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.