Question

2. Draw the graph of the following equations:
(i) 3x – y = 5
(ii) 3x – 4y - 12 =0


with rough work​

Answer 1

EXPLANATION.

Graph of the equation.

⇒ (1) = 3x - y = 5. - - - - - (1).

As we know that,

Put the value of x = 0 in equation, we get.

⇒ 3(0) - y = 5.

⇒ - y = 5.

⇒ y = -5.

Their Co-ordinates = (0,-5).

Put the value of y = 0 in equation, we get.

⇒ 3x - (0) = 5.

⇒ 3x = 5.

⇒ x = 5/3.

⇒ x = 1.66.

Their Co-ordinates = (1.66,0).

⇒ (2) = 3x - 4y = 12. - - - - - (2).

As we know that,

Put the value of x = 0 in equation, we get.

⇒ 3(0) - 4y = 12.

⇒ - 4y = 12.

⇒ y = -12/4.

⇒ y = -3.

Their Co-ordinates = (0,-3).

Put the value of y = 0 in equation, we get.

⇒ 3x - 4(0) = 12.

⇒ 3x = 12.

⇒ x = 4.

Their Co-ordinates = (4,0).

Answer 2

❍ Given that, the equations are ( 3x - y = 5 )  and ( 3x - 4y - 12 = 0 ).

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To draw the graph for these equations we've to find the co-ordinates first by substituting the values in the linear equation.

Finding co-ordinates for the first equation : -

~ By putting the value of x as 0

$\sf : \; \implies [ \; 3 \times 0 \; ] - y = 5$

$\sf : \; \implies 0 - y = 5$

$\sf : \; \implies y = 0 - 5$

$\sf : \; \leadsto y = - 5$

Henceforth, the co-ordinates are ( 0, -5 )

~By putting the value of y as 0

$\sf : \; \implies 3x - 0 = 5$

$\sf : \; \implies 3x = 5 + 0$

$\sf : \; \implies 3x = 5$

$\sf : \; \implies x = \dfrac{5}{3}$

$\sf : \; \leadsto x = 1.66$

Henceforth, the co-ordinates are ( 1.66 , 0 )

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Finding the co-ordinates for the second equation :-

~Putting the value of x as 0

$\sf : \; \implies [ \; 3 \times 0 \; ] - 4y - 12 = 0$

$\sf : \; \implies 0 - 4y = 0 + 12$

$\sf : \; \implies -4y = 12$

$\sf : \; \implies y = \dfrac{12}{-4}$

$\sf : \; \leadsto y = - 3$

Henceforth, the co-ordinates are ( 0, -3 )

~Putting the value of y as 0

$\sf : \; \implies 3x - [ \; 4 \times 0 \; ] - 12 = 0$

$\sf : \; \implies 3x - 0 - 12 = 0$

$\sf : \; \implies 3x = 0 + 12 + 0$

$\sf : \; \implies 3x = 12$

$\sf : \; \implies x = \dfrac{12}{3}$

$\sf : \; \leadsto x = 4$

Henceforth, the co-ordinates are ( 4 , 0 )