Question

b) The cost (x) for hiring and artist for a stage show for (y) hours is represente
as 2y + x = 20.
Draw the graph 2y + x = 20 on the grid below.
[4]​

Answer 1

The easiest way is to transform this equation to intercept form of straight line.

Intercept form of straight line:

• $\dfrac{x}{a}+\dfrac{y}{b}=1$

where $a$ is the x intercept - where the graph intersects the x axis, and $b$ is the y intercept - where the graph intersects the y axis.

Given that,

$2y + x = 20$

$\longrightarrow \: \dfrac{2}{20}y + \dfrac{x}{20} = 1$

$\longrightarrow \: \dfrac{x}{20} + \dfrac{y}{10} = 1$

On comparing with $\dfrac{x}{a}+\dfrac{y}{b}=1,$ we get,

• $a=20$
• $b=10$

Hence, the graph shall cut the x axis and y axis at 20 and 10 respectively. This information is enough to plot the graph.

Graph: Refer to the attachment.