اگر خط y=x+1
را حول محل تقاطع آن با محور طول ها 15 درجه در جهت مثبت مثلثاتی دوران دهیم معادله خط بدست امده کدام است؟
now i dont want you to give me the answer but explain the question with hints so i can do it myself (in english)

Sure! Let's break down the question into manageable parts with some hints.

1. **Identify the Intersection Point**: First, find the intersection of the line \(y = x + 1\) with the x-axis (where \(y = 0\)). This will give you a point through which you'll be rotating the line.

2. **Determine the Slope of the Original Line**: The slope of the line \(y = x + 1\) is \(1\). This information will help you calculate the new slope after rotation.

3. **Rotation Formula**: To rotate a line by an angle \(\theta\), you can use the following formulas for the new slope \(m'\):
   \[
   m' = \frac{m + \tan(\theta)}{1 - m \tan(\theta)}
   \]
   where \(m\) is the original slope and \(\tan(\theta)\) is the tangent of the rotation angle.

4. **Calculate \(\tan(15^\circ)\)**: You will need the value of \(\tan(15^\circ)\) to plug into the rotation formula.

5. **Write the New Equation**: Once you have the new slope \(m'\), you can use the point of intersection (from step 1) to write the equation of the new line in point-slope form or slope-intercept form.

Try working through these steps, and you'll find the equation of the new line after rotation! If you need more guidance, feel free to ask.

### Questions to Consider:
1. What is the point of intersection of the line with the x-axis?
2. How do you calculate \(\tan(15^\circ)\)?
3. What formula can you use to find the new slope after rotation?
4. How do you write the equation of a line given a slope and a point?
5. What does rotating a line by a certain angle do to its slope?

### Tip:
Keep in mind that when rotating a line, the direction of rotation (positive or negative) affects how you calculate the new slope.

اگر خط y=x+1 را حول محل تقاطع آن با محور طول ها 15 درجه در جهت مثبت مثلثاتی دوران دهیم معادله خط بدست امده کدام است؟

Explore how to find the equation of the line y=x+1 after rotating it 15 degrees about its intersection with the x-axis. This problem involves concepts from analytic geometry and trigonometry, suitable for high school students.

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