Finding the Equation of a Straight Line

The lecture covers the general equation of a straight line, explaining the significance of the gradient and y-intercept. It discusses different equation forms and provides examples of calculating gradients and finding line equations. A complex example involving midpoints and line lengths is also explored, concluding with a summary and assessment preparation.

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

• The gradient

• The x-intercept

• The y-intercept

• The constant term

Which equation form is particularly useful when given a gradient and a specific point?

• ax + by + c = 0

• y - y1 = m(x - x1)

• ax + by = c

• y = mx + c

How do you calculate the gradient between two points (x1, y1) and (x2, y2)?

• (x2 - x1) / (y2 - y1)

• (x2 + x1) / (y2 + y1)

• (y2 - y1) / (x2 - x1)

• (y2 + y1) / (x2 + x1)

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

• Calculate the gradient

• Find the y-intercept

• Rearrange the equation

• Calculate the midpoint

How do you find the midpoint of a line segment between two points?

• Add the x-coordinates and y-coordinates separately and divide by 2

• Multiply the x-coordinates and y-coordinates separately and divide by 2

• Subtract the x-coordinates and y-coordinates separately and divide by 2

• Divide the x-coordinates and y-coordinates separately by 2

What is the gradient of a line if the change in y is -22 and the change in x is 11?

• 2

• -2

• 1/2

• -1/2

Which theorem is used to calculate the length of a line segment in a right triangle?

• Archimedes' theorem

• Euclid's theorem

• Newton's theorem

• Pythagoras' theorem