Understanding Linear Equations

In this video, Lucy explains how to find the equation of a straight line passing through two points. She covers finding the gradient using the rise over run method and the formula y2-y1/x2-x1. Lucy then demonstrates using the y=mx+c format to find the y-intercept, even without a graph. The video concludes with a summary and a preview of the next part, which will involve solving without a graph.

What is the first step in finding the equation of a line that passes through two points?

• Find the y-intercept

• Calculate the gradient

• Draw the graph

• Use the quadratic formula

Which formula is used to calculate the gradient of a line?

• x2 - x1 divided by y2 - y1

• y1 - y2 divided by x1 - x2

• y2 - y1 divided by x2 - x1

• x1 + x2 divided by y1 + y2

If the coordinates are (4,3) and (7,9), what is the gradient of the line?

• 1

• 2

• 3

• 4

In the equation y = mx + c, what does 'c' represent?

• The slope

• The gradient

• The x-coordinate

• The y-intercept

How can you find the y-intercept if you don't have a graph?

• By using the quadratic formula

• By substituting known values into the equation

• By using the x-coordinate

• By guessing

What is the y-intercept of the line with the equation y = 2x - 5?

• 5

• -5

• 0

• 2

What is the equation of a line with a gradient of 2 and a y-intercept of -5?

• y = -2x + 5

• y = -2x - 5

• y = 2x + 5

• y = 2x - 5

Why is it not important which coordinates are labeled as 'ones' or 'twos'?

• Because the result is the same

• Because it changes the gradient

• Because it affects the y-intercept

• Because it alters the equation

What is the significance of the gradient in the equation of a line?

• It determines the y-intercept

• It indicates the steepness of the line

• It shows the x-intercept

• It is irrelevant to the line's equation

What will be covered in the next part of the video?

• An introduction to calculus

• A new topic on quadratic equations

• Another example without a graph

• A review of the current example