Slope from Two Points and a Graph

Front

What is the definition of slope?

Back

Slope is a measure of the steepness or incline of a line, typically represented as the ratio of the vertical change to the horizontal change between two points on the line.

Front

How do you calculate the slope (m) from 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?

Back

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

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line falls from left to right.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line where the x-values are the same, resulting in division by zero in the slope formula.

Front

What does a zero slope indicate?

Back

A zero slope indicates a horizontal line where the y-values are the same, meaning there is no vertical change as the x-value changes.

Front

Find the slope of the line passing through the points (2, 3) and (4, 7).

Back

m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

Find the slope of the line passing through the points (1, 2) and (1, 5).

Back

The slope is undefined because the x-values are the same (1).

Front

Find the slope of the line passing through the points (3, 4) and (6, 1).

Back

m = (1 - 4) / (6 - 3) = -3 / 3 = -1.

Front

If a line has a slope of 0, what can you say about its equation?

Back

The equation of the line is of the form y = b, where b is a constant, indicating a horizontal line.