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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.
Solution
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.
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