To find the equation of a line parallel to $y = -2x + 3$ that passes through the point $(1, 5)$, follow these steps:

Step 1: Identify the slope of the given line

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. For the given line: $m = -2$ Parallel lines have the same slope. Thus, the slope of the required line is also $m = -2$.

Step 2: Use the point-slope form of a line

The point-slope form is: $y - y_1 = m(x - x_1)$ Substitute $m = -2$, $x_1 = 1$, and $y_1 = 5$ into the equation: $y - 5 = -2(x - 1)$

Step 3: Simplify the equation

Distribute $-2$ on the right-hand side: $y - 5 = -2x + 2$ Add 5 to both sides: $y = -2x + 7$

Final Answer:

The equation of the required line is: $y = -2x + 7$

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Would you like further clarification or visualization? Here are 5 related questions to expand your understanding:

1. How do you find the slope of a line given two points?
2. What is the difference between parallel and perpendicular lines?
3. How do you convert between point-slope form and slope-intercept form?
4. How can you find the equation of a line passing through two specific points?
5. What happens if you need a line parallel to a vertical or horizontal line?

Tip: For parallel lines, always focus on matching the slope $m$, as that's the defining feature of parallelism!