Finding Slopes Using Graphs and Coordinate Points

Front

What is the slope of a line?

Back

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

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?

Back

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

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines where the change in x is zero, making the slope calculation impossible.

Front

What does a zero slope mean?

Back

A zero slope occurs in horizontal lines where the change in y is zero, indicating that y remains constant as x changes.

Front

Find the slope of the line that passes through (2, 3) and (4, 7).

Back

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

Front

Find the slope of the line that passes through (1, 2) and (3, 2).

Back

The slope is (2 - 2) / (3 - 1) = 0 / 2 = 0 (zero slope).

Front

Find the slope of the line that passes through (5, 5) and (5, 10).

Back

The slope is (10 - 5) / (5 - 5) = 5 / 0, which is undefined.

Front

What is the slope of a line that rises 3 units for every 2 units it runs?

Back

The slope is 3/2.