Slope from a Graph

Front

What is the definition of slope?

Back

Slope is a measure of the steepness 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 from two points (x1, y1) and (x2, y2)?

Back

Slope (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 is a zero slope?

Back

A zero slope indicates a horizontal line where there is no vertical change as the x-value changes.

Front

What is an undefined slope?

Back

An undefined slope occurs with a vertical line where the x-value does not change, leading to division by zero in the slope formula.

Front

If a line rises 3 units and runs 4 units, what is the slope?

Back

Slope = rise/run = 3/4.

Front

If a line falls 5 units and runs 2 units, what is the slope?

Back

Slope = rise/run = -5/2.

Front

What is the slope of a line that goes through the points (1, 2) and (3, 6)?

Back

Slope = (6 - 2) / (3 - 1) = 4/2 = 2.

Front

What is the slope of a line that goes through the points (2, 3) and (2, 5)?

Back

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