In Class 11, the topic of straight lines is introduced in the context of coordinate geometry. Here’s an overview of what you’ll typically study:

1. **Equation of a Straight Line**: The equation of a straight line in the plane can be expressed in various forms, including:

– Slope-intercept form: \(y = mx + c\), where \(m\) is the slope of the line and \(c\) is the y-intercept (the point where the line intersects the y-axis).

– Point-slope form: \(y – y_1 = m(x – x_1)\), where \(m\) is the slope of the line and \((x_1, y_1)\) is a point on the line.

– Two-point form: \(\frac{y – y_1}{y_2 – y_1} = \frac{x – x_1}{x_2 – x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are two points on the line.

2. **Slope of a Line**: The slope of a line is a measure of its steepness. It is given by the ratio of the change in y-coordinates to the change in x-coordinates between two points on the line.

3. **Intercepts**: The x-intercept of a line is the point where it intersects the x-axis (i.e., where \(y = 0\)), and the y-intercept is the point where it intersects the y-axis (i.e., where \(x = 0\)).

4. **Parallel and Perpendicular Lines**: Lines with the same slope are parallel, and lines with slopes that are negative reciprocals of each other are perpendicular.

5. **Distance between a Point and a Line**: The distance between a point \((x_0, y_0)\) and a line \(Ax + By + C = 0\) is given by \(\frac{|Ax_0 + By_0 + C|}{\sqrt{A^2 + B^2}}\).

6. **Angle between Two Lines**: The angle \(\theta\) between two lines with slopes \(m_1\) and \(m_2\) is given by \(\tan(\theta) = \frac{|m_2 – m_1|}{1 + m_1m_2}\).

Understanding the properties and equations of straight lines is fundamental in mathematics and has applications in various fields, including physics, engineering, and computer graphics.

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