Understanding Line Equations and Gradients

This video tutorial explains how to find the equation of a line given its graph. It covers the formula y = mx + c, where m is the gradient and c is the y-intercept. The video demonstrates how to calculate these values using two example problems, showing how to determine the gradient by finding the change in y over the change in x, and identifying the y-intercept directly from the graph. The tutorial provides a clear, step-by-step approach to solving line equations.

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 'm' represent?

• The x-intercept

• The y-intercept

• The gradient

• The constant term

What is the y-intercept of a line?

• The point where the line crosses the x-axis

• The point where the line crosses the y-axis

• The steepness of the line

• The slope of the line

How can you identify the y-intercept on a graph?

• By calculating the slope

• By measuring the angle of the line

• By finding where the line crosses the x-axis

• By finding where the line crosses the y-axis

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

• Change in x divided by change in y

• Change in y divided by change in x

• Difference between x and y

• Sum of x and y

If the change in y is -9 and the change in x is 3, what is the gradient?

• 1/3

• -1/3

• 3

• -3

In the example problem, what is the y-intercept of the line?

• -2

• -3

• 2

• 3

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

• y = -3x - 2

• y = 3x - 2

• y = -3x + 2

• y = 3x + 2

In the second example, what is the y-intercept of the line?

• -3

• 3

• 2

• -2

What is the gradient of the line if the change in y is 1 and the change in x is 4?

• -1/4

• 1/4

• -4

• 4