Everything Maths Grade 10

 4  3  2  1 1 2 3 4

 4

 3

 2

 1

1

2

3

4

0

(0;1)

(2; 2)

(2;4)

 2

 3 #

+2!

+3"

x

y

Worked example 3: Sketching a straight line graph using the gradient–intercept method

QUESTION

Sketch the graph ofp(x) =^12 x 3 using the gradient-intercept method.

SOLUTION

Step 1: Use the intercept

c= 3 , which gives the point(0;3).

Step 2: Use the gradient

m=

change iny

change inx

=

1 "

2!

=

1

2

Start at(0;3). Move 1 unit up and 2 units to the right. This gives the second point(2;2).

Or start at(0;3), move 1 unit down and 2 units to the left. This gives the second point(2;4).

Step 3: Plot the points and draw the graph

 5  4  3  2  1 1 2 3 4 5 6

 5

 4

 3

 2

 1

1

0

(0;3)

(2; 2)

(2;4)

1 "

2!

x

p(x)

Always write the function in the formy=mx+cand take note ofm. After plotting the graph, make sure that
the graph increases ifm > 0 and that the graph decreases ifm < 0.

Chapter 6. Functions 155