**Slope of a line**is the tangent of the angle made by the straight line with positive x-axis in anticlockwise direction. It is denoted by m. If θ be the angle made by the straight line with positive x-axis in anticlockwise direction, then

**slope formula**in terms of angle θ is given by,

Slope
(m) = tanθ

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**Slope of a line joining two given points**

Let A (x

_{1}, y_{1}) and B (x_{2}, y_{2}) be given two points. Join AB, and produce BA to meet x-axis at C so that ∠XCB = θ
Then, slope of CB = slope of AB = m =
tanθ.

From A and B, draw AM and BN
perpendicular to OX. Again from A, draw AD perpendicular to BN.

∠DAB = ∠XCB = θ

Run = AD =
MN = ON – OM = x

_{2}– x_{1}
Rise = DB =
NB – ND = NB – MA = y

_{2}– y_{1}_{}

From the right angled triangle ADB,

Hence, the slope of a line passing through points (x

_{1}, y_{1}) and B (x_{2}, y_{2}) is
This is called

**slope formula**.

*Note:*

*a.*

*The slope of the x-axis and the line parallel to x-axis are zero.*

*b.*

*The slope of the y-axis and the line parallel to y-axis are not defined.*

*c.*

*Two straight lines with equal slopes are parallel to each other.*

*d.*

*If the product of the slopes of two straight lines is -1, then the lines are perpendicular to each other.*

*e.*

*If slope of AB = slope of BC, then the points A, B and C are collinear.*

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*Workout
Examples*

*Workout Examples*

*Example 1: Find the slope of a line whose inclination is 60°.*

*Solution:*

*Here,*

*Inclination (θ) = 60°*

*∴*

*Slope (m) = tanθ*

*= tan60°*

*= √3*

*∴*

*Slope of the line m = √3.*

*Example 2: Find the inclination of a line whose slope is 1.*

*Solution:*

*Here,*

*Slope (m) = 1*

*i.e. tanθ = 1*

*or, tanθ = tan45° [*

*∵*

*tan45° = 1]*

*∴*

*θ = 45°*

*∴*

*Inclination of the line is 45°.*

*Example 3: A straight line passes through the points (3, 2) and (8, 12). Find its slope.*

*Solution:*

*Here,*

*The points are (3, 2) and (8, 12)*

**By the formula,**

*∴*

*Slope of the line m = 2.*

*Example 4:*

*If the slope of a line passing through the points P (2, - 2) and Q (4, a) is -1, find the value of a.*

*Solution:*

*Here,*

*P(2, -2) and Q(4, a)*

*∴*

*x*_{1}= 2 x_{2}= 4

*y*_{1}= -2 y_{2}= a

*Slope (m) = -1*

*∴*

*Value of a is -4.*

*Example 5:*

*If the points (k, 4), (-3, 2) and (3, 5) lie on the same straight line, find the value of k.*

*Solution:*

*Let the given points are A(k, 4), B(-3, 2) and C(3, 5). As the points A, B and C lie on the same straight line,*

*Slope of AB = slope of BC*

*∴*

*Value of k is 1.**You can comment your questions or problems regarding*

**slope of a line**or**slope formula**here.

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