Gradient and Equation of Straight Lines

Front

What is the definition of the gradient of a straight line?

Back

The gradient (or slope) of a straight line is a measure of its steepness, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

Front

How do you calculate the gradient of a line given two points (x1, y1) and (x2, y2)?

Back

The gradient (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the formula for the equation of a straight line in slope-intercept form?

Back

The equation of a straight line in slope-intercept form is y = mx + b, where m is the gradient and b is the y-intercept.

Front

What does the y-intercept of a line represent?

Back

The y-intercept of a line is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

If a line has a gradient of 0, what does this indicate about the line?

Back

A line with a gradient of 0 is horizontal, indicating that there is no change in the y-value as x changes.

Front

What is the significance of a negative gradient?

Back

A negative gradient indicates that the line slopes downwards from left to right, meaning that as x increases, y decreases.

Front

How can you determine which of two lines is steeper?

Back

The steepness of a line can be determined by comparing their gradients; the line with the larger absolute value of the gradient is steeper.

Front

What is the gradient of a vertical line?

Back

The gradient of a vertical line is undefined because the change in x is zero, leading to division by zero in the gradient formula.

Front

How do you find the y-intercept from the equation of a line in standard form (Ax + By = C)?

Back

To find the y-intercept from the standard form, set x = 0 and solve for y.

Front

What is the relationship between parallel lines in terms of their gradients?

Back

Parallel lines have the same gradient, meaning they will never intersect.