Gradient

Front

What is a gradient?

Back

The gradient is a measure of how steep a line is, represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

What does a positive gradient indicate?

Back

A positive gradient indicates that as the x-value increases, the y-value also increases, resulting in an upward slope.

Front

What does a negative gradient indicate?

Back

A negative gradient indicates that as the x-value increases, the y-value decreases, resulting in a downward slope.

Front

What does an undefined gradient mean?

Back

An undefined gradient occurs when a line is vertical, meaning there is no horizontal change (run = 0), making the gradient calculation impossible.

Front

What is the formula for calculating the gradient between two points (x1, y1) and (x2, y2)?

Back

The formula is: Gradient (m) = (y2 - y1) / (x2 - x1).

Front

What is the gradient of a horizontal line?

Back

The gradient of a horizontal line is 0, as there is no vertical change (rise) regardless of the horizontal change (run).

Front

How do you find the y-intercept of a line from its equation?

Back

The y-intercept is the value of y when x = 0. In the equation y = mx + b, b represents the y-intercept.

Front

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

Back

The gradient of the line is 2, which is the coefficient of x.

Front

If a line has a gradient of -3, what does this tell you about its slope?

Back

A gradient of -3 indicates a steep downward slope, meaning for every 1 unit increase in x, y decreases by 3 units.

Front

What is the gradient of the line represented by the equation y = -rac{1}{2}x + 4?

Back

The gradient of the line is -rac{1}{2}, indicating a downward slope.