Slope from Graphs

Front

What is the definition of slope?

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

What does a positive slope indicate about a line?

Back

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

Front

What is an undefined slope?

Back

An undefined slope occurs when a line is vertical, meaning it has no horizontal change (run = 0), resulting in a division by zero.

Front

How do you calculate slope using two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as the x-coordinate changes.

Front

If a line has a slope of -4/3, what does this tell you about its direction?

Back

A slope of -4/3 indicates that for every 4 units the line goes down (rise), it goes 3 units to the right (run), meaning it falls from left to right.

Front

What is the slope of a line that rises 5 units and runs 2 units?

Back

The slope is 5/2.

Front

What is the slope of a line that falls 3 units and runs 1 unit?

Back

The slope is -3/1 or -3.

Front

How can you identify the slope from a graph?

Back

You can identify the slope by selecting two points on the line, calculating the rise (vertical change) and run (horizontal change), and then using the formula slope = rise/run.