The problem asks for the equation of a line in slope-intercept form that passes through a given point and is parallel to a specified line.

Problem Details

The task is to find the slope-intercept form of a line that:

1. Passes through the point $(3, 5)$.
2. Is parallel to the line $y = -2$.

Solution Steps

1. Identify the Slope of the Given Line:

   • The line $y = -2$ is a horizontal line, which has a slope of $0$.
   • Since the new line is parallel to this one, it will also have a slope of $0$.

2. Set Up the Equation Using the Slope-Intercept Form:

   • The slope-intercept form is $y = mx + b$, where $m$ is the slope.
   • Since $m = 0$, our equation so far is: $y = 0 \cdot x + b \Rightarrow y = b$

3. Find the Value of $b$ Using the Given Point $(3, 5)$:

   • Substitute $x = 3$ and $y = 5$ into the equation $y = b$: $5 = b$

4. Write the Final Equation:

   • The equation of the line is: $y = 5$

Answer

The slope-intercept form of the line that passes through $(3, 5)$ and is parallel to $y = -2$ is: $y = 5$

Would you like more details on this solution or have any questions?

Here are some related questions you might find useful:

1. How do you find the slope of a line given two points?
2. What is the general approach for finding a line parallel to a given line?
3. How would you find a line perpendicular to a given line?
4. Can a vertical line be expressed in slope-intercept form?
5. How do you convert between different forms of linear equations?

Tip: For any line parallel to a given one, use the same slope and adjust only the intercept.