Find the equation of the line parallel to the line 2x + 3y = 6 and having a y intercept of 5.2x – 3y = 112x + 3y = 102x + 3y = 152x + 3y = 5

To find the equation of the line parallel to the line $2x + 3y = 6$ and having a y-intercept of 5, we will follow these steps:

1. Break Down the Problem

1. Identify the slope of the given line.
2. Use the y-intercept to establish the equation of the parallel line.

2. Relevant Concepts

• The slope-intercept form of a line is given by the equation:
  $y = mx + b$
  where $m$ is the slope and $b$ is the y-intercept.
• Two lines are parallel if they have the same slope.

3. Analysis and Detail

1. Convert the given line to slope-intercept form: $2x + 3y = 6$
   Rearranging gives:
   $3y = -2x + 6$
   $y = -\frac{2}{3}x + 2$
   The slope $m$ of the line is $-\frac{2}{3}$.

2. Equation of the parallel line: Since the parallel line has the same slope $m = -\frac{2}{3}$ and a y-intercept $b = 5$, we can write its equation as:
   $y = -\frac{2}{3}x + 5$

4. Verify and Summarize

The slope is correctly identified, and the parallel line has been formulated with the correct y-intercept.

Final Answer

The equation of the line parallel to $2x + 3y = 6$ and having a y-intercept of $5$ is:
$y = -\frac{2}{3}x + 5$