8U4L12 - 39 - Slope of a Line on a Coordinate Plane

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the slope-intercept form of a linear equation (y = mx + b). It is calculated as the change in y (rise) over the change in x (run).

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-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 does a slope of zero mean?

Back

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

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines where the change in x is zero, leading to division by zero in the slope formula.

Front

If a line has a slope of 2, what does this mean in terms of rise and run?

Back

A slope of 2 means that for every 1 unit the line moves horizontally (run), it moves 2 units vertically (rise).

Front

What is the slope of a line that runs parallel to the x-axis?

Back

The slope of a line that runs parallel to the x-axis is 0.

Front

What is the slope of a line that runs parallel to the y-axis?

Back

The slope of a line that runs parallel to the y-axis is undefined.

Front

If a line passes through the points (1, 2) and (3, 6), what is the slope?

Back

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