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).

Tags

CCSS.8.EE.B.5

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).

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

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.

Tags

CCSS.8.EE.B.6