Question

If the straight lines 2x+3y−3=0 and x+ky+7=0 are perpendicular, then the value of k is

Answer 1

Given,

2x + 3y - 3 = 0

x + ky + 7 = 0

To Find,

The value of k

Solution,

We can simply solve this mathematical problem using the following mathematical process.

Slope of general equation of line ax + by + c = 0 is m = - $\frac{ Coefficient of x }{ Coefficient of y }$  

Therefore,

Slope of line  2x + 3y - 3 is = -  $\frac{2}{3}$

and

Slope of line x + ky + 7 = 0 is = - $\frac{1}{k}$

Now we know that two lines are perpendicular if their product of slopes is -1

⇒ -$\frac{2}{3}$ × -$\frac{1} {k}$ = - 1

⇒ k =- $\frac{2}{3}$

Hence, the Value of k is -$\frac{2}{3}$

Answer 2

Concept:-

• For any linear equation of line, which is of the form, ax + by + c = 0, it's slope is given by -b/a and slope is represented by m. Therefore we have m = -b/a.
• The product of slopes of two lines which are perpendicular for each other is always equal to -1.

We will use the above mentioned concepts to solve our question.

Solution:-

Let's assume the given lines as:

• L1 : 2x + 3y - 3 = 0
• L2 : x + ky + 7 = 0

As we have discussed the concept of slope above, therefore we can say that:

• Slope of L1 is -3/2
• Slope of L2 = -k/1

Since the lines L1 and L2 are perpendicular to each other the product of their slopes must be -1.

⇒ (-3/2) (-k/1) = -1

⇒ 3k/2 = -1

⇒ 3k = -2

⇒ k = -2/3

Therefore, the required value of k is -2/3.