Question
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Use the equation below to find \( y \), if \( m=3, x=8 \), and \( b=5 \). \[ y=m x-b \] \( y=\square \)

Ask by Bates Phillips. in the United States
Mar 09,2025

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Tutor-Verified Answer

Answer

\( y = 19 \)

Solution

1. Start with the equation: \[ y = m x - b \] 2. Substitute the given values \( m = 3 \), \( x = 8 \), and \( b = 5 \): \[ y = 3 \times 8 - 5 \] 3. Multiply: \[ 3 \times 8 = 24 \] So, \[ y = 24 - 5 \] 4. Subtract: \[ 24 - 5 = 19 \] Thus, the solution is: \[ y = 19 \]

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The Deep Dive

To find \( y \), we can substitute the given values \( m=3 \), \( x=8 \), and \( b=5 \) into the equation \( y=m x-b \): \[ y = 3 \cdot 8 - 5 \] Calculating this gives: \[ y = 24 - 5 = 19 \] So, \( y=19 \). Here's a fun fact: This formula is actually a linear equation representing a straight line on a graph! The slope (m) tells you how steep the line is, while the y-intercept (b) shows where the line crosses the y-axis. To see the real-world application, think about using this equation to model scenarios like budgeting, where \( m \) could represent income per hour, \( x \) could represent hours worked, and \( b \) could be fixed expenses. By tweaking the variables, you can easily forecast savings or spending!

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