Tangents and Normals

Question 1

What is the gradient of a tangent to a point? (compare to gradient of the line)

Answer 1

The gradient of the tangent is the same as the gradient of the line at that point.
m

Question 2

What is the gradient of a normal to a point? (compare to gradient of the line)

Answer 2

The gradient of the normal is the negative reciprocal of the gradient of the line at that point.
-1/m

Question 3

How can you find the gradient?

Answer 3

A) STRAIGHT LINE
when given two coordinates:
(change in y) / (change in x)

B) NOT A STRAIGHT LINE
differentiate the equation of the line at the point
where the tangent/normal touches the line:
nX^(n-1)

Question 4

How do you find the equation of line?

Answer 4

y - y2 = m( x - x2)

Question 5

What is a tangent?

Answer 5

A straight line which touches your graph at one single point.

Question 6

What is a normal?

Answer 6

A straight line which is perpendicular to the tangent of the graph.