Question

To which equation does the graph represent?​

Answer 1

Answer:

(c) 8y - 6x = 4

Step-by-step explanation:

x₁ = 2 , x₂ = -2

y₁ = 2 , y₂ = -1

Slope of graph = M = (y₁ - y₂)/(x₁ - x₂)

⇒ M = (2 - (-1))/(2 - (-2))

⇒ M = (2 + 1)/(2 + 2)

⇒ M = 3/4

now, Equation of graph is :

⇒ y - y₁ = M.(x - x₁)

⇒ y - 2 = 3/4(x - 2)

⇒ 4(y - 2) = 3(x - 2)

⇒ 4y - 8 = 3x - 6

⇒ 4y - 3x = -6 + 8

⇒ 4y - 3x = 2

now, multiply equation by 2.

⇒ 2(4y - 3x) = 2(2)

⇒ 8y - 6x = 4    

Hence, The Equation of Graph is 8y - 6x = 4 .

   

Answer 2

The equation the graph represent is 8y - 6x = 4

Given : The graph of the equation

To find : The equation the graph represent is

(a) 3x - 7y = 10

(b) y - 2x = 3

(c) 8y - 6x = 4

(d) 5x + 35/2y = 25

Solution :

Step 1 of 2 :

Find the points through which the graph passes

The graph passes through the points (2,2) & ( - 2, - 1)

Step 2 of 2 :

Find the equation of the line

The required equation of the line is

$\displaystyle \sf{ \frac{y - 2}{x - 2} = \frac{2 - ( - 1)}{2 - ( - 2)} }$

$\displaystyle \sf{ \implies \frac{y - 2}{x - 2} = \frac{2 + 1}{2 + 2} }$

$\displaystyle \sf{ \implies \frac{y - 2}{x - 2} = \frac{3}{4} }$

$\displaystyle \sf{ \implies 4y - 8 = 3x - 6 }$

$\displaystyle \sf{ \implies 4y - 3x =2 }$

Multiplying both sides by 2 we get

$\displaystyle \sf{ 8y - 6x =4 }$

Hence the correct option is (c) 8y - 6x = 4

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