Everything Maths Grade 10

Worked example 2: Sketching a straight line graph using the dual intercept method

QUESTION

Sketch the graph ofg(x) =x 1 using the dual intercept method.

SOLUTION

Step 1: Examine the standard form of the equation

m > 0. This means that the graph increases asxincreases.

Step 2: Calculate the intercepts

For they-intercept, letx= 0; thereforeg(0) = 1. This gives the point(0;1).

For thex-intercept, lety= 0; thereforex= 1. This gives the point(1; 0).

Step 3: Plot the points and draw the graph

 4  3  2  1 1 2 3 4

 3

 2

 1

1

2

0

g(x) =x 1

(1; 0)

(0;1)

x

y

Gradient andy-intercept method EMA4G

We can draw a straight line graph of the formy=mx+cusing the gradient (m) and they-intercept (c).

We calculate they-intercept by lettingx= 0. This gives us one point(0;c)for drawing the graph and we use
the gradient to calculate the second point.

The gradient of a line is the measure of steepness. Steepness is determined by the ratio of vertical change to
horizontal change:

m=

change iny

change inx

=

vertical change

horizontal change

For example,y=^32 x 1 , thereforem > 0 and the graph slopes upwards.

m=

change iny

change inx

=

3 "

2!

=

3

2

154 6.2. Linear functions