Find the Slope of a Line

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, usually represented as 'm'. It is calculated as the change in the y-coordinate divided by the change in the x-coordinate 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 the x-coordinate increases, the y-coordinate 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-coordinate increases, the y-coordinate decreases, meaning the line falls from left to right.

Front

What does a slope of zero mean?

Back

A slope of zero means the line is horizontal, indicating that there is no change in the y-coordinate as the x-coordinate changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in a vertical line where the x-coordinate does not change, leading to division by zero in the slope formula.

Front

If a line passes through the points (2, 3) and (4, 7), what is the slope?

Back

The slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

What is the slope of a line that goes down from left to right?

Back

The slope is negative.

Front

If a line has a slope of 3, what does this mean in terms of rise over run?

Back

A slope of 3 means that for every 1 unit you move to the right (run), the line rises 3 units (rise).

Front

What is the slope of a line represented by the equation y = 4x + 1?

Back

The slope is 4.