Slope from a Graph

Front

What is the definition of slope in a graph?

Back

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

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 does a positive slope indicate about a line on a graph?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line on a graph?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, meaning the line falls from left to right.

Front

What does a slope of zero indicate?

Back

A slope of zero indicates a horizontal line, meaning there is no vertical change as the x-values change.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the x-values do not change, resulting in a division by zero in the slope formula.

Front

What is the slope of a line that goes through the points (2, 3) and (4, 7)?

Back

The slope is (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

If a line has a slope of -1/2, what does this tell you about the line's direction?

Back

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

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope, meaning they never intersect and maintain a constant distance apart.

Front

What is the relationship between the slopes of perpendicular lines?

Back

Perpendicular lines have slopes that are negative reciprocals of each other, meaning the product of their slopes is -1.