Understanding Linear Equations and Gradients

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 demonstrates how to calculate these values using two example problems, showing how to identify the y-intercept and calculate the gradient by finding the change in y divided by the change in x. The video concludes with a summary of the process.

What is the general form of a straight line equation?

• y = mx + c

• y = mx^2 + c

• y = ax^2 + bx + c

• y = m/x + c

What does the 'c' represent in the equation y = mx + c?

• The slope of the line

• The x-intercept

• The midpoint of the line

• The y-intercept

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

• By finding where the line crosses the x-axis

• By measuring the angle of the line

• By finding where the line crosses the y-axis

• By calculating the slope

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

• Change in y divided by change in x

• Product of x and y changes

• Sum of x and y changes

• Change in x divided by change in y

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

• -1/3

• 3

• 1/3

• -3

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

• y = 3x + 2

• y = 3x - 2

• y = -3x + 2

• y = -3x - 2

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

• Find the x-intercept

• Determine the angle of the line

• Write out the formula y = mx + c

• Calculate the midpoint

If a line passes through points (0, -3) and (4, -2), what is the gradient?

• 1/4

• -1/4

• 4

• -4

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

• y = 1/4x + 3

• y = -1/4x + 3

• y = 1/4x - 3

• y = -1/4x - 3

What is the final step in finding the equation of a line?

• Calculate the midpoint

• Plug the values of m and c into y = mx + c

• Find the x-intercept

• Determine the angle of the line