Use any method to find the point of intersection of \( f(x)=3 x-5 \) and \( g(x)=-4 x+9 \cdot 1 \)-46 HW eTool

Solve the equation \( 3x-5=-4x+9 \). Solve the equation by following steps: - step0: Solve for \(x\): \(3x-5=-4x+9\) - step1: Move the expression to the left side: \(3x+4x=9+5\) - step2: Add and subtract: \(7x=9+5\) - step3: Add and subtract: \(7x=14\) - step4: Divide both sides: \(\frac{7x}{7}=\frac{14}{7}\) - step5: Divide the numbers: \(x=2\) The point of intersection of the functions \( f(x)=3x-5 \) and \( g(x)=-4x+9 \) is at \( x=2 \). To find the corresponding \( y \) value, we can substitute \( x=2 \) into either function. Let's use \( f(x) \): \[ f(2) = 3(2) - 5 = 6 - 5 = 1 \] Therefore, the point of intersection is \( (2, 1) \).