Find the slope and the intercept on the y-axis of the line `sqrt3 x + 3y =6` :

Options

A. a. `-1/sqrt2`, 2
B. b. `1/5`, 3
C. c. `2/sqrt3`, 4
D. d. `-1/sqrt3`, 2

Answer

To find the slope and the intercept on the y-axis of the line given by the equation \( \sqrt{3}x + 3y = 6 \), we will follow these steps:

### Step 1: Rearrange the equation into 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 equation \( \sqrt{3}x + 3y = 6 \).

\[ 3y = -\sqrt{3}x + 6 \]

### Step 2: Divide by 3 to solve for \( y \)
Now, we will divide the entire equation by 3 to isolate \( y \):

\[ y = -\frac{\sqrt{3}}{3}x + 2 \]

### Step 3: Identify the slope and y-intercept
From the equation \( y = -\frac{\sqrt{3}}{3}x + 2 \), we can identify the slope \( m \) and the y-intercept \( c \):

- The slope \( m = -\frac{\sqrt{3}}{3} \)
- The y-intercept \( c = 2 \)

### Final Answer
- Slope: \( -\frac{\sqrt{3}}{3} \)
- Y-intercept: \( 2 \)

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