1. Gradient & Intercept Objectives
(1) Understand the law of straight line
(2)Obtain the standard equation of a straight line

2. The law of a straight line
This is called the standard equation or law of a straight line
M is the gradient and C is the intercept
M= In mathematics the gradient of a line is defined as the tangent of the angle that the line makes with the horizontal and is denoted by the letter m
C is called the intercept on the y axis

3. The method to calculate the gradient
The gradient is also called the slope of a straight line
Gradient
Example Gradient
So the gradient would equal 1

4. Example Gradient
Example Gradient

5. Up is positive, and down is negative
Positive or Negative
How do you identify if is a positive gradient or an negative gradient ?
Starting from the left end of the line going across to the right is positive (but going across to the left is negative).
Up is positive, and down is negative
Example Gradient
That line goes down as you move along, so it has a negative Gradient.

6. Y intercept of a straight line
The Y intercept of a straight line is simply where the line crosses the Y axis.
In the above diagram the line crosses the Y axis at 1.
The Y intercept is equal to 1.

7. Summarise X= Y= M= Value of X horizontally C= Value of Y vertically
Gradient (change in y over change in x)
Intercept on the y axis

8. Straight Line Graphs
Worksheet 1 Depth of cut = x and power in watts = y
Using the table above plot the graph and state the gradient and intercept
Find the value of depth of cut when the power is 1.2 watts from your graph confirm your answer using the gradient formula.
Depth (X)
-0.5
0.51
1.02
1.52
2.03
2.54 3
Power (Y)
0.63
0.76
0.90
1.04
1.17
1.31
1.45
1.57

9. Solve a linear equation by plotting a straight-line graph using experimental data and use it to deduce the gradient, intercept and the equation of the line
1. The table below gives the test results for the measurement of temperature using two digital thermometers one calibrated for Fahrenheit and the other in Centigrade. Plot a graph of the temperatures F in Fahrenheit against the temperatures C in Centigrade and so determine the equation connecting F and C.
2. Determine the equation of the straight line. Find using the graph the value of F when C is 32.5º and the value of C when F is 66º. F
degrees
40.8
49.9
59.9
67.8 76 87
94.9
103.8 C
4.95
9.95
15.5
19.98
24.9
30.5
34.95
39.95