Slope! Slope! Slope!

Front

What is the definition of slope?

Back

Slope is a measure of the steepness or incline of a line, typically represented as 'm' in the equation of a line. It is calculated 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 a positive slope indicate about a line?

Back

A positive slope indicates that as you move from left to right along the line, the line rises. This means that the y-values increase as the x-values increase.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as you move from left to right along the line, the line falls. This means that the y-values decrease as the x-values increase.

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 you move along the line.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x (run) is 0, which would involve division by zero.

Front

If a line has a slope of 4, what does this mean in terms of rise and run?

Back

A slope of 4 means that for every 1 unit you move horizontally (run), the line rises 4 units vertically (rise).

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope of the line is 2, which is the coefficient of x in the equation.

Front

How can you determine if a slope is positive, negative, zero, or undefined from a graph?

Back

You can determine the slope by observing the direction of the line: if it rises from left to right, it's positive; if it falls, it's negative; if it's horizontal, it's zero; and if it's vertical, it's undefined.

Front

What is the slope of the line that passes through the points (1, 2) and (3, 6)?

Back

The slope is calculated as m = (6 - 2) / (3 - 1) = 4 / 2 = 2.