The equation representing the given graph is _____.

7 x + 2 y = 11; y - 2 x = 3

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2 x + 7 y = 11; 5 x + (35 y / 2) = 25

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3 x - 7 y = 10; 8 y - 6 x = 4

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3 x - 4 y = 1; 8 y - 6 x = 4

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Solution

The correct option is C $3 x - 4 y = 1; 8 y - 6 x = 4$
Recall equation of line using two points,
$y - y_{1} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} (x - x_{1})$
Lets take two points and form equation for the line fitting this data,
$L i n e_{1}$
$(x_{1}, y_{1}) = (- 2, - 1)$
$(x_{2}, y_{2}) = (2, 2)$
Equation becomes,
$y - (- 1) = \frac{2 - (- 1)}{2 - (- 2)} (x - (- 2))$
$y + 1 = \frac{3}{4} (x + 2)$
$3 x - 4 y = - 2$
$6 x - 8 y = - 4$
$8 y - 6 x = 4$

$L i n e_{2}$
$(x_{1}, y_{1}) = (- 1, - 1)$
$(x_{2}, y_{2}) = (3, 2)$
Equation becomes,
$y - (- 1) = \frac{2 - (- 1)}{3 - (- 1)} (x - (- 1))$
$y + 1 = \frac{3}{4} (x + 1)$
$3 x - 4 y = 1$

Answer: $3 x - 4 y = 1, 8 y - 6 x = 4$

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