Suppose \( y=3 x-5 \). Find \( y \) if: \( x=\frac{1}{3} \) \( y=\square \)

To find \( y \) when \( x = \frac{1}{3} \), we substitute \( x \) into the equation \( y = 3x - 5 \): \[ y = 3\left(\frac{1}{3}\right) - 5 \] \[ y = 1 - 5 = -4 \] So, \( y = -4 \). If we wanted to play around with this expression, we could see how the value of \( y \) changes with different values of \( x \). For example, if \( x \) were to increase by 1 unit, \( y \) would increase by 3 units, showcasing a linear relationship! Understanding linear equations can really help in making sense of real-life situations. For instance, if this equation represented the cost of items in a shop, where \( 3x \) might represent the total cost based on the number of items bought, and \( -5 \) is a discount, you can visualize how spending changes drastically with even marginal increases in purchases!