# Question #34eca

Dec 19, 2016

The equation of given straight line is $2 x + y = 3 \mathmr{and} y = - 2 x + 3$

So its slope ${m}_{1} = - 2$

Hence slope of any straight line perpendicular to it is ${m}_{2} = - \frac{1}{m} _ 1 = - \left(- \frac{1}{2}\right) = \frac{1}{2}$

If the second straight line passes through $\left(- 7 , 8\right)$ its equation will be

$y - 8 = {m}_{2} \left(x - \left(- 7\right)\right)$

$\implies y - 8 = \frac{1}{2} \left(x + 7\right)$

$\implies y - 8 = \frac{x}{2} + \frac{7}{2}$

$\implies y = \frac{x}{2} + \frac{7}{2} + 8$

$\implies y = \frac{x}{2} + \frac{23}{2}$