Gradients

1
Gradients
2
Straight line gradients

• The gradient is the slope of a straight line. It
  measures how steep a line rises or falls.

The greater the gradient, the steeper the slope
or incline.
3

• The symbol for gradient is the letter m. If
  the line is sloping upwards the gradient will be
  positive. If the line is sloping downwards, the
  gradient will be negative.

-m
m
Line sloping upwards positive gradient.
Line sloping downwards negative gradient.
4
Finding the Gradient

• To find the gradient of a line, we use this
  formula

Gradient Change in Y m Y2 Y1
Change in X X2 X1
5
Example

• Find the gradient of the line joining (-1,2)
  and (3,-1).

4
2
4
2
6
-2
-2
This line is sloping downwards, therefore it is a
negative gradient.
-4
6
Answer

• Answer Gradient change in
  Y
• 
  change in X
• m Y2 Y1 -1-2
  -3
• X2 X1
  3- -1 4
• When the X coordinates of the line are the
  same, the line will be vertical. We say that the
  gradient of a vertical line is undefined.
• Exercise
  16.3 page 130.
• 
  Homework exercise 18.03 page 79.

7
Gradient Trigonometry

• This is where the gradient of the line makes an
  angle with the x axis, T

The gradient of this line is the fraction. But
from trig tan T
C D
C D
co
To
do
8

• If follows that if that if we know the angle
  that a line makes with the positive direction of
  the x axis, the gradient of the line will be tan
  of this angle. And if we know the gradient of a
  line, we can use trig (tan-1) to calculate the
  angle between the line and the x-axis.

9
Example

• A line makes and angle of 40o with the x-axis, as
  shown in the diagram. Calculate the gradient of
  the line.

Gradient tan40 0.84
Work in class Ex 16.4, page 131 Homework Ex
18.04, page 79.
40o