Question

Find the value of m, If the two lines

3mx - 2my - 10 = 0 and

(5m + 2)x - 4my - 28 = 0 are parallel.

a) m=3
b) m=2
c) m=4
d) m=7​

Answer 1

Answer:

m = 2     (option b)

Step-by-step explanation:

They must have same slope to be parallel. On comparing these equations with y = mx + c, where m is the slope.(don't be confused by m), this represents slope, whereas your represents a constant value.

For 1st line,  3mx - 2my - 10 = 0

⇒ y = (3m/2m)x - (10/m)

Slope is 3m/2m = 3/2

For the 2nd line,(5m + 2)x - 4my - 28 = 0

⇒ y = (5m+2)x/4m - (28/4m)

Slope is (5m + 2)/4m

To be parallel, both must be equal,

⇒ (5m + 2)/4m = 3/2

⇒ 2(5m + 2) = 3(4m)

⇒ 10m + 4 = 12m

⇒ 4 = 2m

⇒ 2 = m

Answer 2

Given :-

3mx - 2my - 10 = 0 and

(5m + 2)x - 4my - 28 = 0 are parallel.

Solution :-

In the 1st slope

(3m/2m)x - (10/m)

3m/2m

m = 3/2

In the 2nd slope

(5m+2)x/4m - (28/4m)

5m +2x/4m

On comparing

(5m + 2)/4m = 3/2

• Cross multiplication

2(5m + 2) = 3(4m)

10m + 4 = 12m

12m - 10m = 4

2m = 4

m = 4/2

m = 2