Three ordered pair of an equation is given as follows: $x$ $y$

1 3

2 12

Find the linear equation.

y = 5 x + 3

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y = 5 x - 3

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It cannot be determined as three ordered pairs are required to find the values of three unknowns in

a x + b y = c .

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Solution

The correct option is B $y = 5 x - 3$
The slope form of linear equation with two variables is $y = m x + c$

where, $m$ is the slope of the line.

$m = \frac{change in y}{change in x} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Substituting the ordered pairs
$m = \frac{12 - 2}{3 - 1}$
$\Rightarrow m = \frac{10}{2}$
$\Rightarrow m = 5$

$∴$ Equation is $y = 5 x + c$
By substituting one of the ordered pair,
$2 = 5 (1) + c$
$\Rightarrow 2 - 5 = c$
$\Rightarrow c = - 3$

Hence, the required equation is $y = 5 x - 3.$

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