Slope/Unit Rate

Front

What is the definition of slope?

Back

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

Front

How do you calculate the slope between 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 unit rate?

Back

A unit rate is a ratio that compares a quantity to one unit of another quantity, often expressed as 'per' something.

Front

If a car travels 150 miles in 3 hours, what is the unit rate of speed?

Back

The unit rate is 50 miles per hour (150 miles / 3 hours).

Front

What is the slope of a line that goes through the points (2, 3) and (4, 7)?

Back

Slope = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

Which line has a slope of 0?

Back

A horizontal line has a slope of 0 because there is no vertical change as the x-value changes.

Front

What is the slope of a vertical line?

Back

A vertical line has an undefined slope because the change in x is 0, leading to division by zero.

Front

How can you determine which line is the steepest?

Back

The steepness of a line can be determined by comparing the absolute values of their slopes; the larger the absolute value, the steeper the line.