2) Find the equetion of line pory to \( 5 x-y=-4 \)

To find the equation of the line that is parallel to the given line \(5x - y = -4\), we first need to determine the slope of the original line. Rewriting the equation in slope-intercept form (y = mx + b), we get \(y = 5x + 4\). The slope (m) here is 5. Since parallel lines share the same slope, the new line will also have a slope of 5. You can express the new line in slope-intercept form as \(y = 5x + b\), where \(b\) is the y-intercept that you can choose based on your specific requirements. To make it even more exciting, let's say you wanted the new line to pass through the point (2, 3). You would plug these values into the slope-intercept form: \(3 = 5(2) + b\), which gives you \(b = -7\). Therefore, the equation of the parallel line passing through (2, 3) would be \(y = 5x - 7\)! Now, how about exploring some common mistakes in such problems? A frequent pitfall is forgetting that parallel lines have identical slopes, which can lead to using a different slope when trying to find the parallel line equation. Always take a moment to verify the slope of your original line before moving forward! Another common mistake is not translating the standard form of the equation properly into slope-intercept form; this makes understanding the relationship between lines trickier than it needs to be.