Gradient and Equation of a Line

The video tutorial explains how to find the equation of a line given a graph. It introduces the formula y=mx+c, where m is the gradient and c is the y-intercept. The tutorial provides two examples, demonstrating how to calculate the gradient using the change in y divided by the change in x, and how to identify the y-intercept. The video concludes with a summary of the process.

What is the general form of a straight line equation?

• y = ax + b

• y = a/x + b

• y = ax^2 + bx + c

• y = mx + c

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

• The midpoint of the line

• The y-intercept

• The x-intercept

• The slope of the line

How can you find the y-intercept of a line on a graph?

• By finding where the line crosses the x-axis

• By finding where the line crosses the y-axis

• By calculating the slope

• By measuring the length of the line

What is the formula to calculate the gradient of a line?

• Difference between x and y

• Change in x divided by change in y

• Change in y divided by change in x

• Sum of x and y

If a line crosses the y-axis at y = 2, what is the value of c?

• 3

• 2

• 1

• 0

Given two points on a line, (1, 5) and (4, 2), what is the gradient?

• -1

• 3

• -3

• 1

What is the equation of a line with a gradient of -3 and y-intercept of 2?

• y = 3x - 2

• y = -3x - 2

• y = -3x + 2

• y = 3x + 2

For a line with points (0, -3) and (4, -2), what is the gradient?

• 4

• 2

• 1/2

• 1/4

What is the equation of a line with a gradient of 1/4 and y-intercept of -3?

• y = -1/4x + 3

• y = 1/4x + 3

• y = -1/4x - 3

• y = 1/4x - 3

What is the first step in finding the equation of a line from a graph?

• Calculate the gradient

• Identify the y-intercept

• Draw a triangle

• Write the equation in y = mx + c form