Finding Slope

Front

What is the definition of slope?

Back

Slope is a measure of the steepness or incline of a line, typically represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

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).

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it goes straight up and down and does not have a defined rise over run.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning it does not rise or fall as it moves from left to right.

Front

Find the slope of the line passing through the points (1, 2) and (3, 6).

Back

The slope is 2, calculated as (6 - 2) / (3 - 1).

Front

Find the slope of the line passing through the points (-4, 5) and (-4, 2).

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 3 units for every 4 units it runs?

Back

The slope is 3/4.

Front

If a line has a slope of -1, what does this indicate about its direction?

Back

A slope of -1 indicates that the line descends from left to right at a 45-degree angle.

Front

How do you determine the slope from a table of values?

Back

To determine the slope from a table, calculate the change in y (rise) divided by the change in x (run) between two points.

Front

Find the slope of the line represented by the equation y = 4x + 1.

Back

The slope is 4, which is the coefficient of x in the equation.