Understanding Normal Lines and Their Equations

The video tutorial explains the concept of normal lines, which are perpendicular to tangent lines. It covers the steps to find the normal line using the negative reciprocal of the derivative. Two examples are provided: one to find the normal line equation at a specific point, and another abstract question involving gradients. The tutorial emphasizes understanding the relationship between tangent and normal lines and how to calculate their slopes.

What is the relationship between the slopes of perpendicular lines?

• They are both negative.

• They are both positive.

• They are negative reciprocals of each other.

• They are equal.

If a line has a slope of 3, what is the slope of a line perpendicular to it?

• -3

• 1/3

• -1/3

• 3

What is the first step in finding the normal line to a curve?

• Find the x-intercept.

• Find the derivative of the function.

• Find the y-intercept.

• Find the slope of the tangent line.

How do you find the slope of the normal line once you have the slope of the tangent line?

• Subtract 1.

• Take the negative reciprocal.

• Add 1.

• Multiply by 2.

In Example 1, what is the y-coordinate of the point where x = 4?

• 2

• 5

• 3

• 4

What is the slope of the normal line in Example 1?

• -1/2

• 1/4

• 1/2

• -1/4

What is the equation of the normal line found in Example 1?

• y = -1/4x + 4

• y = -1/4x + 3

• y = 1/4x + 3

• y = 1/4x + 4

In Example 2, what is the gradient of the tangent line if the gradient of the normal line is -1/4?

• -1/4

• 1/4

• 4

• -4

What is the value of K in Example 2?

• 1

• 2

• 3

• 4

What is the y-coordinate B in Example 2 when x = 1?

• 0

• 1

• 2

• 3