Question

find the equation of the straight line passing through the point (2,5) and parallel to the line passing through (2,5) and (-3,6)​

Answer 1

SOLUTION

TO DETERMINE

The equation of the straight line passing through the point (2,5) and parallel to the line passing through (2,5) and (-3,6)

EVALUATION

Here the equation of the line passing through the points (2,5) and (-3,6) is

$\displaystyle \sf{ \frac{y - 6}{x + 3} = \frac{6 - 5}{ - 3 - 2} }$

$\implies \displaystyle \sf{ \frac{y - 6}{x + 3} = \frac{1}{ - 5} }$

$\implies \displaystyle \sf{x + 3 = - 5y + 30 }$

$\implies \displaystyle \sf{x + 5y = 27 } \: \: \: ......(1)$

Now the equation of the line parallel to Equation (1) is

$\displaystyle \sf{x + 5y = c } \: \: \: .....(2)$

Now the line (2) passes through the point (2,5)

$\implies \displaystyle \sf{2 + (5 \times 5) =c }$

$\implies \displaystyle \sf{2 +25 =c }$

$\implies \displaystyle \sf{c = 27 }$

Hence the required equation of the line is

$\sf{x + 5y = 27}$

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