To understand the equation of a line which is parallel to x axis,

To understand the equation of a line which is parallel to y axis,

**Question 1 :**

Find the equation of a straight line passing through the mid-point of a line segment joining the points (1, -5) , (4, 2) and parallel to :

(i) X axis (ii) Y axis

**Solution :**

Midpoint of the line segment = (x_{1} + x_{2})/2, (y_{1} + y_{2})/2

= (1 + 4)/2 , (-5 + 2)/2

= (5/2, -3/2)

(i) The required line is passing through the point (5/2, -3/2) and parallel to x axis.

If the line is parallel to x-axis, then slope of the required line = 0.

(y - y_{1}) = m (x - x_{1})

y + (3/2) = 0(x - (5/2))

(2y + 3) /2 = 0

2y + 3 = 0

So, the required line parallel to x-axis is

2y + 3 = 0

(ii) The required line is passing through the point (5/2, -3/2) and parallel to x axis.

If the line is parallel to y-axis, then slope of the required line = undefined.

(y - y_{1}) = m (x - x_{1})

y + (3/2) = (1/0)(x - (5/2))

x - (5/2) = 0

2x - 5 = 0

So, the required line parallel to y-axis is

2x - 5 = 0

**Question 2 :**

The equation of a straight line is 2(x −y)+ 5 = 0 . Find its slope, inclination and intercept on the Y axis.

**Solution :**

2(x - y) + 5 = 0

2x - 2y + 5 = 0

2y = 2x + 5

y = (2/2)x + (5/2)

y = x + (5/2)

Slope (m) = 1

Angle of inclination :

m = 1

tan θ = 1

θ = 45^{0}

Intercept of y - axis :

y-intercept (c) = 5/2

**Question 3 :**

Find the equation of a line whose inclination is 30˚ and making an intercept -3 on the Y axis.

**Solution :**

θ = 30˚

m = tanθ

m = tan 30 = 1/√3

intercept on y - axis = -3

**Equation of the line :**

y = m x + c

y = (1/√3)x + (-3)

y = (x/√3) - (3√3)

√3y = x - 3√3

x - √3y - 3√3 = 0

**Question 4 :**

Find the slope and y intercept of √3x + (1 − √3)y = 3

**Solution :**

**√3x +(1 − √3)y = 3**

By comparing the given equation with the form y = mx + c, we get slope and y-intercept.

**(1 − √3)y = 3 - ****√3x**

**y = (-****√3x + 3)/****(1 − √3)**

**y = [-****√3****/****(1 − √3)] ****x + 3/****(1 − √3)**

**Slope = -****√3****/****(1 − √3) **

** = [ ****√3****/****(****√3-****1) ] ****(****√3+****1)/****(****√3+****1)**

** = ****√3****(****√3+****1)****/****(****√3-****1)****(****√3+****1)**

** ****= (3 + ****√3)****/2**

y-intercept = **3/****(1 − √3)**

** = [****3/****(1 − √3)][(1 + ****√3)/(1+****√3)]**

** = 3(1+****√3)/(1 - 3)**

** = (-3 - 3****√3)/2**** **

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