Find the equation of the line passing through (2,-11) that is parallel to the line 4x + 3y = 7.
+45 we find the slope of the line:
\(\begin{align*} 4x+3y&=7\\ 3y&=-4x+7\\ y&=-\frac{4}{3}x+7 \end{align*}\)
and plug in the \(x\) and \(y\) of \((2, -11)\) to find the \(y \)-intercept:
\(\begin{align*} y &= -\frac{4}{3}x + b \\ -11 &= -\frac{4}{3}(2)+b \\ -11 &= -\frac{8}{3} + b \\ b &= -\frac{25}{3} \end{align*}\)
and plug in the slope for
\(\boxed{y=-\frac{4}{3}x-\frac{25}{3}}.\)
