Find the equation of the line with slope `2/3` and intercept on the y-axis is 5 :

Options

A. `y=2/3 x+5`
B. `y=3/2 x +5`
C. `y=3x +6`
D. none of these

Answer

To find the equation of the line with a given slope and y-intercept, we can use the slope-intercept form of a linear equation, which is expressed as:

\[ y = mx + c \]

Where:
- \( m \) is the slope of the line,
- \( c \) is the y-intercept.

### Step-by-Step Solution:

**Step 1: Identify the slope and y-intercept.**
- The slope \( m \) is given as \( \frac{2}{3} \).
- The y-intercept \( c \) is given as \( 5 \).

**Step 2: Substitute the values into the slope-intercept form.**
- We substitute \( m \) and \( c \) into the equation \( y = mx + c \):

\[ y = \frac{2}{3}x + 5 \]

**Step 3: Write the final equation.**
- The equation of the line is:

\[ y = \frac{2}{3}x + 5 \]

### Final Answer:
The equation of the line is \( y = \frac{2}{3}x + 5 \).