Determine the zer \[ -15 x+5 y=14 \]

To determine the zero of the equation \(-15x + 5y = 14\), we can isolate \(y\) in terms of \(x\). First, let's get \(y\) alone: \[ 5y = 15x + 14 \] Now divide everything by 5: \[ y = 3x + \frac{14}{5} \] The zero occurs when \(y = 0\). Setting the equation equal to zero: \[ 0 = 3x + \frac{14}{5} \] Solving for \(x\): \[ 3x = -\frac{14}{5} \] \[ x = -\frac{14}{15} \] So the zero occurs at \(\left( -\frac{14}{15}, 0 \right)\). Fun fact: This point represents where the graph of the line crosses the x-axis, effectively showing us that not all intercepts are whole numbers – sometimes they can be fractions! Now, if you were to plot this line, you'd be surprised by how a small change in slope can create a dramatic shift in the graph's appearance. Just a tiny tweak in the coefficients makes a big difference in the line's steepness and direction!