1. Find the slope of the line 
(a) Making inglination of  60% with x axis 
(b) Passion through the point (3, -3) and (-1,4)

Let's solve each part of this problem.

### Part (a)
1. **Finding the Slope Given an Inclination with the X-Axis**:
   The inclination (angle) of a line with the \( x \)-axis is given as \( 60^\circ \).
   
   The slope \( m \) of a line inclined at an angle \( \theta \) with the \( x \)-axis is calculated using:
   \[
   m = \tan(\theta)
   \]

2. **Applying the Angle**:
   Here, \( \theta = 60^\circ \). So,
   \[
   m = \tan(60^\circ) = \sqrt{3}
   \]

   **Answer for (a):** The slope of the line is \( \sqrt{3} \).

---

### Part (b)
1. **Finding the Slope Between Two Points**:
   Given points are \( (3, -3) \) and \( (-1, 4) \).

2. **Using the Slope Formula**:
   The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]

   Substituting \( (x_1, y_1) = (3, -3) \) and \( (x_2, y_2) = (-1, 4) \):
   \[
   m = \frac{4 - (-3)}{-1 - 3} = \frac{4 + 3}{-4} = \frac{7}{-4} = -\frac{7}{4}
   \]

   **Answer for (b):** The slope of the line passing through \( (3, -3) \) and \( (-1, 4) \) is \( -\frac{7}{4} \).

---

Would you like more details on these solutions, or do you have any questions?

### Related Questions

1. How is the slope of a line defined geometrically?
2. What is the relationship between inclination and slope for different angles?
3. How would you find the angle if given only the slope?
4. Can a line have an undefined slope? If so, under what conditions?
5. How do parallel and perpendicular slopes relate in terms of values?

**Tip:** Always remember that the slope of a line inclined at \(90^\circ\) with the x-axis is undefined since \( \tan(90^\circ) \) is undefined.

1. Find the slope of the line 
(a) Making inclination of 60° with x-axis 
(b) Passing through the points (3, -3) and (-1,4)

Learn how to find the slope of a line with a 60° inclination to the x-axis and through two points, (3, -3) and (-1, 4). This solution covers key concepts in geometry and trigonometry, using the slope formula and the tangent function for inclination. Ideal for students in Grades 9-10.

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