Coordinate Geometry Concepts and Applications

This video tutorial covers coordinate geometry, focusing on plotting points, finding equations of lines by inspection, analyzing volume changes over time, drawing lines with given gradients, calculating gradients, and deriving line equations from points. The tutorial provides step-by-step guidance and encourages viewers to practice and verify their understanding through examples and exercises.

What is the correct equation of a line that passes through the points P, Q, R, and S?

• x + y = 3

• y = 3x + 1

• y = x - 3

• x - y = 3

What is the change in volume for every minute the tap is left on?

• -40 liters

• -30 liters

• -10 liters

• -20 liters

What is the gradient of a line with a rise of 2 and a run of 5?

• 2/5

• 0

• 5/2

• -2/5

What is the gradient of the line through the points (2, 1) and (8, 13)?

• 2

• 1/2

• -2

• 2/3

What is the equation of a line with a gradient of 1/4 and passes through the point (3, 5)?

• y = 1/4x + 4.25

• y = 1/4x - 4.25

• y = 4x + 1

• y = -1/4x + 5

Do the points (-2, 5) lie on the line y = -2x + 1?

• Insufficient information

• Only if x is negative

• No

• Yes

What is the y-intercept of the line y = 3/4x - 3?

• -3

• 3/4

• 3

• 0

What is the equation of a line with x-intercept 4 and y-intercept 3?

• y = -4x + 3

• y = 4x + 3

• y = 3/4x - 3

• y = -3/4x + 3

What is the gradient of a line that goes through the points (-2, 2) and (0, 4)?

• -1

• 0

• 2

• 1

For a line with a gradient of 3/2 and a y-intercept of -3, what is the equation?

• y = 3/2x - 3

• y = -3/2x + 3

• y = 2/3x - 3

• y = 3x - 2/3