Question

Draw the graph of the equation 2x - 3y - 5 = 0
From the graph, find:
(i) x₁, the value of x, when y = 7
(ii) x₂, the value of x, when y = - 5.

Answer 1

2x - 3y - 5 = 0
⇒ 2x = 3y + 5
⇒ x = `(3y + 5)/(2)`

When y = 1,
x = `(3(1)+5)/(2)`
= `(8)/(2)`
= 4

When y = 3,
x = `(3(3)+5)/(2)`
= `(9 + 5)/(2)`
= 7

When y = - 1,
x = `(3(-1)+5)/(2)`
= `(5 - 3)/(2)`
= 1

X	4	7	1
Y	1	3	- 1

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

(i) The value of x, when y = 7:

We have the equation of the line as 

x = `(3y + 5)/(2)`

Now substitute y = 7 and x = x₁:
x₁ = `(3(7) + 5)/(2)`

= `(21 + 5)/(2)`

= `(26)/(2)`
= 13

(ii) The value of x, when y = - 5:

Now substitute y = - 5 and x = x₂

x₂ = `(3(-5) + 5)/(2)`

= `(-15 + 5)/(2)`

= `(-10)/(2)`

 = -5.