Slopey Slope

Front

What is the definition of slope?

Back

Slope is a measure of the steepness of a line, calculated as the ratio of the rise (vertical change) to the run (horizontal change) between two points on the line.

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for slope (m) is: m = (y2 - y1) / (x2 - x1).

Front

If a line has a slope of 2, what does this indicate about the line's steepness?

Back

A slope of 2 indicates that for every 1 unit the line moves horizontally to the right, it moves 2 units vertically up.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change (rise) regardless of the horizontal change (run).

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the run is 0, leading to division by zero in the slope formula.

Front

How do you determine if two lines are parallel based on their slopes?

Back

Two lines are parallel if they have the same slope.

Front

How do you determine if two lines are perpendicular based on their slopes?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

Calculate the slope of the line that passes through the points (1, 2) and (3, 6).

Back

The slope is 2, calculated as (6 - 2) / (3 - 1).

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line is decreasing; as you move from left to right, the line goes down.

Front

What is the slope of the line represented by the equation y = 3x + 1?

Back

The slope of the line is 3, which is the coefficient of x in the equation.