**Equation of the Line Parallel to x and y Axis :**

Here we are going to see, some example problems to show finding equation of the line parallel to x and 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

Hence the require 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

Hence 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**** **

After having gone through the stuff given above, we hope that the students would have understood, "Equation of the Line Parallel to x and y Axis".

Apart from the stuff given in this section "Equation of the Line Parallel to x and y Axis", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**