Find the equation of the line perpendicular to y=−5/9x that passes through (−7,3)

Find the equation of the line perpendicular to $y=-\frac{5}{9}x$ that passes through (−7,3)
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One of the forms of the equation of a straight line is y = mx + c where m represents the gradient and c , the y-intercept.
the line $y=-\frac{5}{9}x$
is in this form with c = 0 and m = $-\frac{5}{9}$
When 2 lines are perpendicular then the product of their gradients :
${m}_{1}{m}_{2}=-1$
The gradient of the perpendicular line is : $-\frac{5}{9}×{m}_{2}=-1$
$⇒{m}_{2}=-\frac{1}{-\frac{5}{9}}=\frac{9}{5}$
equation : y - b = m(x - a ) , m = $\frac{9}{5},\left(a,b\right)=\left(-7,3\right)$
$⇒y-3=\frac{9}{5}\left(x-7\right)$
multiply both sides by 5 to eliminate fraction : $5y-15=9x-63$
equation of perpendicular line is 5y - 9x + 48 = 0