Understanding Gradients and Lines

What is the primary purpose of connecting two points with a line on a Cartesian plane?

• To determine the midpoint of the line

• To measure the distance between the points

• To show relationships or changes over time

• To calculate the area of the plane

If the x-axis represents time, what does the gradient of a line indicate?

• The total distance covered

• The rate of change over time

• The maximum value reached

• The average speed

In the context of the video, what does a steeper line indicate about cake sales?

• Fewer cakes are sold over a longer period

• The sales decrease over time

• More cakes are sold in less time

• The sales remain constant

How do you calculate the gradient of a line using two points?

• Divide the x-values by the y-values

• Multiply the x-values and y-values of the points

• Add the x-values and y-values of the points

• Subtract the y-values and divide by the difference in x-values

What happens to the gradient if the difference between the x-values is larger than the difference between the y-values?

• The gradient becomes negative

• The gradient remains the same

• The gradient becomes gentler

• The gradient becomes steeper

What does a negative gradient indicate about the direction of a line's slope?

• The line slopes downwards to the right

• The line is vertical

• The line is horizontal

• The line slopes upwards to the right

If two lines have gradients of 1, what can be said about their slopes?

• They are horizontal

• They are vertical

• They have a 45° slope

• They are parallel

What is the relationship between two lines that have the same gradient?

• They are perpendicular

• They are parallel and do not intersect

• They intersect at one point

• They form a right angle

What does it mean if a line has a gradient of zero?

• The line is parallel to the y-axis

• The line is vertical

• The line is horizontal

• The line is at a 45° angle

Which letter is commonly used to represent the gradient of a line?

• N

• L

• M

• G