Slope (graphs, tables, points)

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 to the horizontal change between two points on the line.

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 an undefined slope?

Back

An undefined slope occurs when a line is vertical, meaning there is no horizontal change (x2 - x1 = 0), making the slope calculation impossible.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no vertical change as the x-value changes.

Front

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

Back

A slope of 2 means that for every 1 unit increase in x, the y-value increases by 2 units.

Front

What is the slope of the line represented by the equation y = 3x + 1?

Back

The slope of the line is 3, which is the coefficient of x in the equation.

Front

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

Back

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

Front

What is the slope of the line that passes through the points (1, 2) and (3, 8)?

Back

Slope = (8 - 2) / (3 - 1) = 6 / 2 = 3.