2 Find the equation of a line paralle) to \( y=1 / 3 x-4 \) and passiog through \( (5,0) \)

To find the equation of a line parallel to \( y = \frac{1}{3}x - 4 \) that passes through the point \( (5, 0) \), we need to use the fact that parallel lines have the same slope. The slope of the given line is \( \frac{1}{3} \). Now, using the point-slope form of a line equation: \[ y - y_1 = m(x - x_1) \] where \( m \) is the slope, and \( (x_1, y_1) \) is the point the line passes through, we have: \[ y - 0 = \frac{1}{3}(x - 5) \] Simplifying gives: \[ y = \frac{1}{3}x - \frac{5}{3} \] So, the equation of the required line is \( y = \frac{1}{3}x - \frac{5}{3} \). Remember, lines can be like best friends—you can have as many as you want as long as they stick to the same direction! The key takeaway here is how we use the slope to maintain the parallelism. One common mistake while solving this is forgetting to apply the point-slope formula properly. It helps to always double-check that you've plugged in the correct point and used the correct slope from the original line!