Slope & Comparing Rates of Change Review

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

How do you determine which line has a higher slope?

Back

To determine which line has a higher slope, compare the coefficients of x in the equations of the lines. The line with the larger coefficient has a steeper slope.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the change in x is zero, leading to division by zero in the slope formula.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no change in y as x changes.

Front

How do you find the slope between two points?

Back

The slope between two points (x1, y1) and (x2, y2) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as 'b' in the equation y = mx + b.

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.

Front

What does it mean if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, indicating they intersect at a right angle.

Front

How can you represent a rate of change in a real-world context?

Back

A rate of change can be represented by the slope of a line on a graph, such as speed (distance over time) or cost per item.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.