If x and y are related by 2x+3y+4=0 and SD of x is 9, then SD of y is

Option b: 6. Solution: Given: 2x + 3y + 4 = 0, SD(x) = 9 Step 1: Express y in terms of x. 3y = -2x - 4 y = -2/3x - 4/3 Step 2: Find SD of y. For y = a + bx: SD(y) = |b| SD(x) Here b = -2/3: SD(y) = <=ft|-2/3right| x 9 = 2/3 x 9 = 6 Hence, Option B is the correct answer.

If $x$ and $y$ are related by $2x+3y+4=0$ and SD of $x$ is $9$, then SD of $y$ is

The correct answer is Option b: $6$. **Given:** $2x + 3y + 4 = 0$, $SD(x) = 9$ **Step 1: Express $y$ in terms of $x$.** $$3y = -2x - 4$$ $$y = -\frac{2}{3}x - \frac{4}{3}$$ **Step 2: Find SD of $y$.** For $y = a + bx$: $SD(y) = |b| \cdot SD(x)$ Here $b = -\frac{2}{3}$: $$SD(y) = \left|-\frac{2}{3}\right| \times 9 = \frac{2}{3} \times 9 = 6$$ Hence, **Option B** is the correct answer.

Central Tendency & DispersionMTP May 20Question 3164 of 473

All Questions

If $\displaystyle x$ and $\displaystyle y$ are related by $\displaystyle 2x+3y+4=0$ and SD of $\displaystyle x$ is $\displaystyle 9$ , then SD of $\displaystyle y$ is

Options

\displaystyle 22

\displaystyle 6

\displaystyle 5

\displaystyle 24

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Correct Answer

✅ Option b — $\displaystyle 6$

All Options:

A $\displaystyle 22$
B $\displaystyle 6$
C $\displaystyle 5$
D $\displaystyle 24$

Detailed Solution & Explanation

**Given:**

\displaystyle 2x + 3y + 4 = 0

\displaystyle SD(x) = 9

**Step 1: Express

\displaystyle y

in terms of

\displaystyle x

.**

3y = -2x - 4

y = -\frac{2}{3}x - \frac{4}{3}

**Step 2: Find SD of

\displaystyle y

.** For

\displaystyle y = a + bx

\displaystyle SD(y) = |b| \cdot SD(x)

Here

\displaystyle b = -\frac{2}{3}

SD(y) = \left|-\frac{2}{3}\right| \times 9 = \frac{2}{3} \times 9 = 6

Hence, **Option B** is the correct answer.

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If x\displaystyle xx and y\displaystyle yy are related by 2x+3y+4=0\displaystyle 2x+3y+4=02x+3y+4=0 and SD of x\displaystyle xx is 9\displaystyle 99, then SD of y\displaystyle yy is