Question What is an equation of the line that passes through the point \( (-8,-1) \) and is parallel to the line \( x-2 y=18 \) ?

To find an equation of the line that passes through the point \( (-8,-1) \) and is parallel to the line \( x - 2y = 18 \), we first need to determine the slope of the original line. Rearranging it into slope-intercept form \( y = mx + b \), we find that the slope \( m \) is \( \frac{1}{2} \). Since parallel lines share the same slope, our new line will also have a slope of \( \frac{1}{2} \). Next, we can use the point-slope form of a line, which is \( y - y_1 = m(x - x_1) \), where \( (x_1, y_1) \) is the point \( (-8, -1) \). Plugging in the values, we get: \[ y - (-1) = \frac{1}{2}(x - (-8)) \] \[ y + 1 = \frac{1}{2}(x + 8) \] \[ y + 1 = \frac{1}{2}x + 4 \] \[ y = \frac{1}{2}x + 3 \] Therefore, the equation of the line is \( y = \frac{1}{2}x + 3 \). Now go grab a pencil and graph it—you’ll be drawing a parallel line that climbs gently at a slope of \( \frac{1}{2} \), crossing the y-axis at 3! Happy graphing! ✏️📊 Understanding the relationship between parallel lines is also super useful in real-life contexts! For example, if you’re planning a road trip and want to ensure your paths remain at a constant angle with respect to the earth's surface, parallel line concepts can help in trajectory calculations. Whether it’s highways or designs for buildings, these principles come into play! 🚗🏗️