A line with slope `(2)/(3)` is translated up 5 units and right 1 unit. What is the slope of new line?

Answer

To solve the problem, we need to understand how translating a line affects its slope.

1. **Identify the original slope**: The original slope of the line is given as \( \frac{2}{3} \).

2. **Understand the translation**: The problem states that the line is translated (moved) up by 5 units and to the right by 1 unit.

3. **Determine the effect of translation on slope**: When a line is translated, its slope remains unchanged. This is because translating a line does not alter its angle with respect to the axes; it simply shifts the entire line to a new position.

4. **Conclusion**: Since the slope of the original line is \( \frac{2}{3} \) and translating it does not change the slope, the slope of the new line after translation is still \( \frac{2}{3} \).

Thus, the slope of the new line is \( \frac{2}{3} \).