**Slope-intercept form:**

The slope-intercept form of the equation of a line is y = mx + b, where m is the slope of the line and b is the y-intercept of the line.

The y-intercept of a line is the y-co-ordinate of the point at which the line intersects the y-axis. Likewise, the x-intercept of a line is the x-co-ordinate of the point at which the line intersects the x-axis. Therefore, if the slope-intercept form of the equation of a line is given, we can find both intercepts. For example, in order to find the y-intercept, simply set x = 0 and solve for the value of y. For the x-intercept, set y = 0 and solve for x.

If both the x-intercept and y-intercept of a line is given, then the equation of the line is x/a + y/b = 1, where a is the x-intercept and b is the y-intercept.**Point-slope form:** The point-slope form of the equation of a line is 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:** The equation of a line passing through the points (x

_{1}, y

_{1}) and (x

_{2}, y

_{2}) is given by,

### Angle between two lines

- If m
_{1}and m_{2}are the slopes of two lines, the angle θ between them is given by, - If a
_{1}x + b_{1}y + c_{1}= 0 and a_{2}x + b_{2}y + c_{2}= 0 are equations of two lines, the angle θ between them is given by, - If a
_{1}x + b_{1}y + c_{1}= 0 and a_{2}x + b_{2}y + c_{2}= 0 are equations of two lines, then these two lines are parallel when, - If a
_{1}x + b_{1}y + c_{1}= 0 and a_{2}x + b_{2}y + c_{2}= 0 are equations of two lines, then these two lines are perpendicular to each other when,

a_{1}a_{2}+ b_{1}b_{2}= 0

**Condition for parallel lines**a

_{1/}a

_{2}= b

_{1/}b

_{2}or m

_{1}= m

_{2}

**Condition for perpendicular lines**

a

_{1}a

_{2}+ b

_{1}b

_{2}= 0 or m

_{1}m

_{2}= -1

**Area of the triangle**

Area of the triangle formed by the vertices A(x_{1}, y_{1}), B(x_{2}, y_{2}), C(x_{3}, y_{3}) is given by,If the area of the triangle is zero, then it indicates that the three points A, B and C are collinear i.e. lie on the same straight line.

**Section formula**

i. Internal Division:

2. External Division:

**Equations of circle**

The equation of a circle centred at (h, k) with radius ‘r’ units is: (x - h)

^{2}+ (y - k)

^{2}= r

^{2}

The equation of a circle centred at the origin with radius ‘r’ units is: x

^{2}+ y

^{2}= r

^{2}

**Centroid of a triangle**

**Circumcentre of a triangle**

OA

^{2}= OB

^{2}= OC

^{2}

(x - x

_{1})

^{2}+ (y - y

_{1})

^{2}= (x - x

_{2})

^{2}+ (y - y

_{2})

^{2}= (x - x

_{3})

^{2}+ (y - y

_{3})

^{2}

Where, A, B and C are the vertices of the triangle and O is the circumcenter.

**Incentre of a triangle**