1. Chapter 2: The Straight Line and Applications
Measure Slope and Intercept Figures Slide 2,4
Different lines with (i) same slopes, (ii) same intercept. Slide 3.
How to draw a line, given slope and intercept. Worked Example 2.1 Figure 2.6, Slide 5
What is the equation of a line ? Illustrated by Figure 2.9.
Slides nos
Write down the equation of a line, given its slope and intercept, Worked Example 2.2, Figure 2.9
OR given the equation, write down the slope and intercept
Slides no. 17, 18, 19
Plot a line by joining the intercepts. Slide no.20, 21, 22
Equations of horizontal and vertical lines, Figure 2.11: Slide no. 23

2. Measuring Slope and Intercept
The point at which a line crosses the vertical axis is referred as the ‘Intercept’
Slope =
intercept = 2 4 3 2
intercept = 0 1 -4 -3 -2 -1 1 2 3 4 -1 -2 -3
intercept = - 3
Line AB
slope =
Line CD
slope = -4
Figure 2.6 -5

3. Slope alone or intercept alone does not define a line
Lines with same intercept but different slopes are different lines
Lines with same slope but different intercepts are different lines

4. A line is uniquely defined by both slope and intercept
In mathematics, the vertical intercept is referred to by the letter c
In mathematics, the slope of a line is referred to by the letter m
Intercept, c = 2
slope, m = 1

5. Draw the line, given slope =1: intercept = 2 Worked Example 2.1(b)
The graph of the line which has
intercept = 2, slope = 1
1. Plot a point at intercept = 2
2. From the intercept draw a line with slope = 1 by
(a) moving horizontally forward by one unit and
(b) vertically upwards by one unit
3. Extend this line indefinitely in either direction, as required
Figure 2.6 (
1, 3)
(0, 2) x

6. What does the equation of a line mean
Consider the equation y = x
From the equation, calculate the values of y for
x = 0, 1, 2, 3, 4, 5, 6.
The points are given in the following table. x y
Plot the points as follows

7. x y 1 2 3 4 5 6 x y
(0, 0)
Plot the point x = 0, y = 0

8. x y
Plot the point x = 1, y = 1 6 5 4 3 y 2
(1, 1) 1
(0, 0) x 1 2 3 4 5 6

9. x y
Plot the point x = 2, y = 2 6 5 4 3 y
(2, 2) 2
(1, 1) 1
(0, 0) x 1 2 3 4 5 6

10. x y
Plot the point x = 3, y = 3 6 5 4
(3, 3) 3 y
(2, 2) 2
(1, 1) 1
(0, 0) x 1 2 3 4 5 6

11. x y
Plot the point x = 4, y = 4 6 5 4
(4, 4)
(3, 3) 3 y
(2, 2) 2
(1, 1) 1
(0, 0) x 1 2 3 4 5 6

12. x 0 1 2 3 4 5 6 y 0 1 2 3 4 5 6 Plot the point x = 5, y = 5 6 (5, 5) 5
(4, 4)
(3, 3) 3 y
(2, 2) 2
(1, 1) 1
(0, 0) x 1 2 3 4 5 6

13. x 0 1 2 3 4 5 6 y 0 1 2 3 4 5 6 Plot the point x = 6, y = 6 6 (6, 6)
(5, 5) 5 4
(4, 4)
(3, 3) 3 y
(2, 2) 2
(1, 1) 1
(0, 0) x 1 2 3 4 5 6

14. Join the plotted points
x y
Join the plotted points 6
(6, 6)
(5, 5) 5 4
(4, 4)
(3, 3) 3 y
(2, 2) 2
(1, 1) 1
(0, 0) x 1 2 3 4 5 6

15. The y co-ordinate = x co-ordinate, for every point on the line:
x y
The y co-ordinate = x co-ordinate, for every point on the line: 6
(6, 6)
(5, 5) 5 4
(4, 4)
(3, 3) 3 y
(2, 2) 2
(1, 1) 1
(0, 0) x 1 2 3 4 5 6
Figure The 45o line, through the origin

16. y = x is the equation of the line.
x y
y = x is the equation of the line. 6
(6, 6)
(5, 5) 5 4
(4, 4)
(3, 3) 3 y
(2, 2) 2
(1, 1) 1
Similar to Figure 2.9
(0, 0) x 1 2 3 4 5 6

17. Deduce the equation of the line, given slope, m = 1; intercept, c = 2
1. Determine and plot at least 2 points:
2. Start at x = 0, y = 2 (intercept, c=2)
3. Since slope = 1, move forward 1unit then up 1 unit. See Figure 2.6
Hence the point (x = 1, y = 3)
4. Deduce further points in this way
5. Observe that value of the y co-ordinate is always (value of the x co-ordinate +2):
Hence the equation y = x+ 2
6. That is, y = (1)x + 2
In general, y = mx + c
is the equation of a line
(0, 2) (
1, 3) x y
(2, 4)
Figure 2.6

18. Deduce the equation of the line, given slope, m = 1; intercept, c = 2
Use Formula y = mx + c
Since m = 1, c = 2 , then
y = mx + c y = 1x + 2
y = x + 2
See Figure 2.6
(0, 2) (
1, 3) x y
(2, 4)
Figure 2.6

19. The equation of a line
The equation of a line may be written in terms of the two characteristics, m (slope) and c (intercept) . y = mx + c
Example:
y = x is a line which has a slope = 1, intercept = 0
y = x + 2 is the line which has a
slope = 1 , intercept = 2
Putting it another way:
the equation of a line may be described as the formula that allows you to
calculate the y co-ordinate for any point on the line, when given the value of the x co-ordinate.

20. Calculating the Horizontal Intercepts
Calculate the horizontal intercept for the line: y = mx + c
The horizontal intercept is the point where the line crosses the x -axis
Use the fact that the y co-ordinate is zero at every point on the x-axis.
Therefore, substitute y = 0 into the equation of the line
0 = mx + c
and solve for x:
0 = mx + c: therefore, x = -c/m
This is the value of horizontal intercept
Line: y = mx + c
(m > 0: c > 0)
y = mx + c
Intercept = c
Slope = m
0, 0
Horizontal intercept = - c/m

21. Determine the slope and intercepts for a line when the equation is given in the form: ax + by +d = 0
Rearrange the equation into the form y = mx + c:
Slope = : intercept =
Horizontal intercept =
Example:4x + 2y - 8 = 0
Slope = -2: intercept = 4
Horizontal intercept =

22. Plot the line 4x+2y - 8 = 0 by calculating the horizontal and vertical intercepts:
Rearrange the equation into the form y = mx + c
y = -2x + 4
Vertical intercept at y = 4
Horizontal intercept at x = 2 (see previous slide)
Plot these points: see Figure 2.13
Draw the line thro’ the points
Figure 2.13

23. Equations of Horizontal and vertical lines:
The equation of a horizontal is given by the point of intersection with the y-axis
The equation of a vertical line is given by the point of intersection with the x -axis
Figure 2.11