Slope from a Graph

Front

What is slope?

Back

Slope is a measure of the steepness or incline of a line, typically represented as a 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 the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as there is no horizontal change.

Front

If a line rises 4 units for every 2 units it runs, what is the slope?

Back

Slope = rise/run = 4/2 = 2.

Front

What type of slope does the line in the graph have if it goes down from left to right?

Back

The line has a negative slope.

Front

If a line has a slope of 3/2, what does this mean?

Back

This means that for every 2 units the line moves horizontally, it rises 3 units vertically.

Front

What is the slope of a line that travels 32 miles for every gallon of gasoline used?

Back

The slope is 32, representing the miles traveled per gallon.