Question
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
Ask by Pollard Bond. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The point of intersection is \( (2, 1) \).
Solution
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 \( (2, 1) \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To find the point of intersection of the functions \( f(x) = 3x - 5 \) and \( g(x) = -4x + 9 \), we set them equal to each other: \[ 3x - 5 = -4x + 9 \] Now, let's solve for \( x \). First, add \( 4x \) to both sides: \[ 3x + 4x - 5 = 9 \] This simplifies to: \[ 7x - 5 = 9 \] Next, add \( 5 \) to both sides: \[ 7x = 14 \] Now, divide by \( 7 \): \[ x = 2 \] Now that we have the \( x \)-coordinate, we can substitute it back into one of the original equations to find the \( y \)-coordinate. Using \( f(x) \): \[ f(2) = 3(2) - 5 = 6 - 5 = 1 \] So, the point of intersection is \( (2, 1) \).
