Understanding Linear Equations and Gradients

This video tutorial explains why line equations are typically written in the form y=mx+c, highlighting the convenience of this format for comparing and graphing lines. It covers the significance of the gradient (m) and y-intercept (c), and demonstrates how to rearrange equations into this form. The tutorial also provides guidance on plotting lines from equations and addresses special cases where equations may lack explicit m or c values.

Why is the equation y = mx + c preferred for graphing lines?

• It is the only correct form.

• It simplifies the comparison of lines.

• It is the oldest form.

• It is easier to memorize.

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

• The x-intercept

• The constant term

• The y-intercept

• The gradient of the line

In the equation y = 2x + 3, what is the y-intercept?

• 1

• 0

• 2

• 3

How do you rearrange the equation 2y - 4x = 6 into the form y = mx + c?

• Add 6 to both sides and divide by 4

• Subtract 6 from both sides and divide by 4

• Subtract 4x from both sides and divide by 2

• Add 4x to both sides and divide by 2

What is the gradient of the line represented by y = 2x + 3?

• 1

• 2

• 0

• 3

What is the first step in rearranging 4y + 16 = 2x to the form y = mx + c?

• Add 16 to both sides

• Divide both sides by 4

• Subtract 16 from both sides

• Multiply both sides by 4

After rearranging 4y + 16 = 2x, what is the y-intercept?

• -4

• 4

• 2

• 0

If an equation lacks a 'c' value, what can be assumed?

• c is equal to m

• c is undefined

• c is 0

• c is 1

What is the gradient of a line if the equation is y = 3x?

• 1

• Undefined

• 0

• 3

In the equation y = x + 4, what is the gradient?

• 4

• 0

• 1

• x