# CLASSIFYING LINES FROM THE GIVEN EQUATIONS

If two lines are travelling in the same path, then the lines are parallel. Slopes of the lines can be considered as m1 and m2

If two lines are parallel, then their slopes will be equal.

m1 = m2

If two lines are perpendicular, then the product of their slopes is equal to -1

m1 x m2 = -1

Problem 1 :

Classify the pair of equations.

-3x + y = 11

y - 29 = 3(x - 6)

i)  The same line

ii) Distinct parallel lines

iii) Perpendicular lines

iv) Intersecting but not perpendicular lines

Solution :

Given, -3x + y = 11 and y - 29 = 3(x - 6)

-3x + y = 11

y = 3x + 11

Slope intercept equation of a line y = mx + b, we get

m = slope

m1 = 3

y - 29 = 3(x - 6)

y - 29 = 3x - 18

y = 3x - 18 + 29

y = 3x + 11

m2 = 3

The slopes are m1 = 3 and m2 =  3.

Since, the slope of the lines m1 and m2 are parallel.

So, option ii) is correct.

Problem 2 :

Classify the pair of equations.

-x + y = 8

y - 5 = (x + 3)

Solution :

Given, -x + y = 8 and y - 5 = (x + 3)

-x + y = 8

y = x + 8

Slope intercept equation of a line y = mx + b, we get

m = slope

m1 = 1

y - 5 = (x + 3)

y = 5(x + 3)

y = 5x + 15

m2 = 5

The slopes are m1 = 1 and m2 =  5.

Since, the slope of the lines m1 and m2 are neither.

Problem 3 :

Classify the pair of equations.

3x + 2y = -20

y + 22 = -3/2(x - 8)

Solution :

Given, 3x + 2y = -20 and y + 22 = -3/2(x - 8)

3x + 2y = -20

2y = -3x - 20

Slope intercept equation of a line y = mx + b, we get

m = slope

m1 = -3/2

m2 = -3/2

The slopes are m1 = -3/2 and m=  -3/2.

Since, the slope of the lines m1 and m2 are parallel.

Problem 4 :

Classify the pair of equations.

-x + 5y = -5

5x + y = 48

Solution :

Given, -x + 5y = -5 and 5x + y = 48

-x + 5y = -5

5y = x - 5

Slope intercept equation of a line y = mx + b, we get

m = slope

m1 = 1/5

5x + y = 48

y = - 5x + 48

m2 = -5

The slopes are m1 = 1/5 and m2 =  -5.

= 1/5 × -5

= -1

Since, the slope of the lines m1 and m2 are perpendicular.

Problem 5 :

Classify the pair of equations.

-8x - 9y = -27

24x + 27y = 81

Solution :

Given, -8x - 9y = -27 and 24x + 27y = 81

-8x - 9y = -27

-9y = 8x - 27

9y = -(8x - 27)

9y = -8x + 27

Slope intercept equation of a line y = mx + b, we get

m = slope

m1 = -8/9

24x + 27y = 81

27y = -24x + 81

m2 = -8/9

The slopes are m1 = -8/9 and m=  -8/9.

Since, the slope of the lines m1 and m2 are parallel.

Problem 6 :

Classify the pair of equations.

9x - 10y = -10

-9x + 10y = 10

Solution :

Given, 9x - 10y = -10 and -9x + 10y = 10

9x - 10y = -10

-10y = -9x - 10

10y = -(-9x - 10)

10y = 9x + 10

Slope intercept equation of a line y = mx + b, we get

m = slope

m1 = 9/10

-9x + 10y = 10

10y = 9x + 10

m2 = 9/10

The slopes are m1 = 9/10 and m2 =  9/10.

Since, the slope of the lines m1 and m2 are parallel.

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