The slope of straight line `sqrt(3)y=3x+4` is

Options

A. 3
B. `sqrt(3)`
C. `(1)/(sqrt(3))`
D. `(1)/(3)`

Answer

To find the slope of the straight line given by the equation \(\sqrt{3}y = 3x + 4\), we will follow these steps:

### Step 1: Rewrite the equation in slope-intercept form
The slope-intercept form of a line is given by the equation:
\[ y = mx + c \]
where \(m\) is the slope and \(c\) is the y-intercept. We need to isolate \(y\) in the given equation.

Starting with:
\[ \sqrt{3}y = 3x + 4 \]

### Step 2: Divide both sides by \(\sqrt{3}\)
To isolate \(y\), we divide both sides of the equation by \(\sqrt{3}\):
\[ y = \frac{3}{\sqrt{3}}x + \frac{4}{\sqrt{3}} \]

### Step 3: Simplify the fraction
Now, we simplify \(\frac{3}{\sqrt{3}}\):
\[ \frac{3}{\sqrt{3}} = \sqrt{3} \]
Thus, the equation becomes:
\[ y = \sqrt{3}x + \frac{4}{\sqrt{3}} \]

### Step 4: Identify the slope
From the equation \(y = \sqrt{3}x + \frac{4}{\sqrt{3}}\), we can identify the slope \(m\):
\[ m = \sqrt{3} \]

### Final Answer
The slope of the straight line \(\sqrt{3}y = 3x + 4\) is \(\sqrt{3}\).

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