Slope - Multiple Representations

Front

What is slope?

Back

Slope is a measure of the steepness of a line, calculated as the change in the vertical direction (rise) divided by the change in the horizontal direction (run).

Front

How do you calculate slope from a table of values?

Back

To calculate slope from a table, use the formula: Slope (m) = (y2 - y1) / (x2 - x1) using two points (x1, y1) and (x2, y2) from the table.

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

Front

What is the y-intercept?

Back

The y-intercept is the point where a line crosses the y-axis, representing the value of y when x is 0.

Front

What does the y-intercept represent in a real-world context?

Back

In a real-world context, the y-intercept often represents the starting value of a quantity before any changes occur.

Front

How can you find the y-intercept from a table?

Back

The y-intercept can be found by identifying the value of y when x is 0 in the table.

Front

What is the slope of a line that rises 3 units for every 1 unit it runs?

Back

The slope is 3, calculated as rise/run = 3/1.

Front

If a line has a slope of 0, what does that mean?

Back

A slope of 0 means the line is horizontal, indicating that there is no change in y as x changes.

Front

What is the slope of a line that falls 2 units for every 4 units it runs?

Back

The slope is -1/2, calculated as rise/run = -2/4.