Question

if the line Y = 3 X + 7 and 2 Y + 3 x =3 are perpendicular to each other find the value of p​

Answer 1

Given that,

lines y = 3x + 7 and 2y + px = 3 are perpendicular to each other

Step 1:

Find the slope of each line

The equation of line is:

y = mx + c

Where,

"m" is the slope and "c" is the y intercept

From given,

y = 3x + 7

Coefficient of x is 3

Thus,

$m_1=3$

Similarly,

$\begin{gathered}2y + px = 3\\\\2y = -px - 3\\\\y = \frac{-px}{2} -\frac{3}{2}\end{gathered}$

$\begin{gathered}coefficient\ of\ x = \frac{-p}{2} \\\\Thus \\\\m_2 = \frac{-p}{2}\end{gathered}$

We know,

When two lines are perpendicular, then product of their slopes is always equal to -1

Thus,

$\begin{gathered}m_1 \times m_2 = -1\\\\3 \times \frac{-p}{2} = -1\\\\p = \frac{2}{3}\end{gathered}$

Thus, value of p is 2/3

Answer 2

Answer:

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