Find the zero of the linear function. \[ f(x)=\frac{2}{3} x-10 \]

To find the zero of the linear function \( f(x) = \frac{2}{3}x - 10 \), we set \( f(x) \) to zero and solve for \( x \): \[ 0 = \frac{2}{3}x - 10 \] Adding 10 to both sides gives: \[ 10 = \frac{2}{3}x \] Next, we multiply both sides by \(\frac{3}{2}\) to isolate \( x \): \[ x = 10 \times \frac{3}{2} = 15 \] So, the zero of the function is \( x = 15 \). --- Did you know that linear functions like this one represent straight lines on a graph? The point where the line crosses the x-axis (the zero) is particularly important because it tells us where the function's value changes from positive to negative or vice versa! In real life, linear functions are everywhere, from calculating distance over time to budgeting expenses! Understanding how to find zeros can help you in fields like economics, physics, and even engineering, as it enables you to identify break-even points or equilibrium states.