8.3.c: Slope (All Forms)

Front

What is the slope?

Back

The slope is a measure of the steepness or incline of a line, typically represented as a ratio of the vertical change to the horizontal change between two points.

Front

What are the types of slope?

Back

There are three main types of slope: Positive (rising line), Negative (falling line), and Zero (horizontal line). Undefined slope occurs when a vertical line is present.

Front

How do you write the equation of a line given a starting fee and a rate per hour?

Back

The equation can be written in the form y = mx + b, where m is the rate per hour and b is the starting fee.

Front

Find the slope between the points (-4, 3) and (-4, -7).

Back

The slope is Undefined because the x-coordinates are the same, indicating a vertical line.

Front

What is the slope of a line that rises 2 units for every 1 unit it runs?

Back

The slope is 2, which can be expressed as 2/1.

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in an upward trend.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward trend.

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-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is Undefined because there is no horizontal change.

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).