Equation Of Parallel Lines

In this video, Lucy explains how to find the equation of parallel lines. She begins by reviewing the y = mx + c format and the concept of gradient. Lucy illustrates that parallel lines have the same gradient and demonstrates how to find the equation of a parallel line passing through a given point. She provides a step-by-step example, showing how to substitute coordinates to find the y-intercept. The video concludes with a summary and a prompt to explore perpendicular lines in another video.

What is the key characteristic of parallel lines in terms of their gradient?

• Their gradients are zero.

• Their gradients are negative reciprocals.

• They have the same gradient.

• They have different gradients.

If a line has the equation y = 3x + 4, what is the gradient of a line parallel to it?

• 0

• -3

• 4

• 3

Given a line y = 2x + 6, what is the equation of a parallel line passing through the point (4, -2)?

• y = 2x + 10

• y = 2x - 10

• y = 2x + 2

• y = 2x - 2

What is the y-intercept of a line parallel to y = -2x + 5 that passes through the point (1, -1)?

• 0

• 1

• -1

• 5

Which of the following steps is necessary to find the equation of a parallel line?

• Find the y-intercept using a given point.

• Calculate the slope using two points.

• Change the gradient.

• Use the midpoint formula.