Calculating Slope

Front

What is slope?

Back

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

Front

What is the formula for calculating slope?

Back

The formula for slope (m) is: m = \frac{y_2 - y_1}{x_2 - x_1} where (x_1, y_1) and (x_2, y_2) are two points on the line.

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 does a zero slope indicate?

Back

A zero slope indicates a horizontal line where there is no change in the y-value as the x-value changes.

Front

What does an undefined slope indicate?

Back

An undefined slope occurs in a vertical line where the x-value remains constant, leading to a division by zero in the slope formula.

Front

How do you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, find the vertical change (rise) and the horizontal change (run), and use the formula m = \frac{rise}{run}.

Front

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

Back

The slope is 2, calculated as m = \frac{6 - 2}{3 - 1} = \frac{4}{2} = 2.

Front

If a line has a slope of 3, what does this mean?

Back

A slope of 3 means that for every 1 unit increase in the x-direction, the y-value increases by 3 units.

Front

What is the slope of a line parallel to the line y = 2x + 1?

Back

The slope of a line parallel to y = 2x + 1 is 2, as parallel lines have the same slope.