The problem in the image asks to write the equation of a line parallel to the line $2x + y = 3$ and passing through the point (-2, 5).

Steps to solve:

1. Find the slope of the given line: The given line is $2x + y = 3$. We can rewrite it in slope-intercept form $y = mx + b$, where $m$ is the slope.

   $y = -2x + 3$

   So, the slope of the line is $m = -2$.

2. Use the same slope for the parallel line: Lines that are parallel have the same slope. Therefore, the line we need to find will also have a slope of $-2$.

3. Use the point-slope form of a line: The point-slope form of a line is: $y - y_1 = m(x - x_1)$ where $(x_1, y_1)$ is the point the line passes through, and $m$ is the slope. In this case, the point is $(-2, 5)$ and the slope $m = -2$.

   Substituting the values: $y - 5 = -2(x + 2)$

4. Simplify the equation: Expanding and simplifying the equation: $y - 5 = -2x - 4$ $y = -2x + 1$

So, the equation of the line parallel to $2x + y = 3$ and passing through $(-2, 5)$ is: $y = -2x + 1$

Would you like any further details or explanations?

5 Related Questions:

1. What is the slope of a line perpendicular to $2x + y = 3$?
2. How do you convert a line equation from standard form to slope-intercept form?
3. What is the point-slope form, and when is it used?
4. How do you write the equation of a line perpendicular to another line?
5. How do you determine if two lines are parallel or perpendicular?

Tip:

When given a line equation in standard form, always rearrange it into slope-intercept form to easily identify the slope for parallel or perpendicular line problems.