Question

Draw the graph of the equation
4x + 3y + 6 = 0
From the graph, find :
(i) y₁, the value of y, when x = 12.
(ii) y₂, the value of y, when x = - 6.

Answer 1

4x + 3y + 6 = 0
⇒ 3y = -4x - 6
⇒ y = `(-4x - 6)/(3)`

When x = 0,
y = `(-4(0)-6)/(3)`
= `(-6)/(3)`
= -2
When x = 3,
y = `(-4(3)-6)/(3)`
= `(-12 -6)/(3)`
= -6
When x = -3,
y = `(-4(3)-6)/(3)`
= `(12 -6)/(3)`
= 2

X	0	3	-3
Y	-2	-6	2

Plotting these points we get the required graph as shown below:

The value of y, when x = 12:
We have the equation of the line as
y = `(- 4x - 6)/3`

Now substitute x = 12 and y = y₁:
y₁ = `(-4(12)-6)/(3)`

= `(-48 - 6)/(3)`

= `(-54)/(3)`
= - 18

The value of y, when x = - 6:
Now substitute x = - 6 and y = y₂:
y₂ = `(-4(-6)-6)/(3)`

= `(24 - 6)/(3)`

= `(18)/(3)`
= 6