How do you find a standard form equation for the line with point (9, -9) and is parallel to the line 7x-9y+5 = 0?

1 Answer
Jul 28, 2016

$y = \frac{7}{9} x - 16$

Explanation:

Rewrite the given equation as:

${y}_{1} = \frac{7}{9} {x}_{1} + \frac{5}{9}$

The gradient being $+ \frac{7}{9}$ so any line parallel to this will have the same gradient.

Thus for the new line we have: ${y}_{2} = \frac{7}{9} {x}_{2} + c$.....................Equation(1)

Given that a point on this line is:$\text{ } {P}_{1} \to \left({x}_{2} , {y}_{2}\right) = \left(9 , - 9\right)$

Thus by substituting ${P}_{1}$ into Equation(1) we have:
$- 9 = \frac{7}{\cancel{9}} \left(\cancel{9}\right) + c$

$\implies c = - 9 - 7 = - 16$

Giving:$\text{ } {y}_{2} = \frac{7}{9} {x}_{2} - 16$