Question

If the lines y = 3x + 7 and 2y + px = 3 are perpendicular to each other, find the value of p.

Answer 1

Answer:

Step-by-step explanation:

Standard equation is y=m*x+c and slope is m.

If two lines are perpendicular multiplication of the slopes equal to -1.

So, y=3*x+7

Here slope is 3

2*y+p*x=3

y=(3-p*x)/2

y=-p/2*x+3/2

Here sloe is -p/2

Both lines are pependicular so,

(-p/2)*3=-1

-p=(-1)*2/3

p=2/3

Answer 2

If the lines y = 3x + 7 and 2y + px = 3 are perpendicular to each other, value of p is 2/3

Solution:

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,

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

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

We know,

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

Thus,

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

Thus, value of p is 2/3

Learn more:

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