Final answer:
To find the equation of a line parallel to y = 2x + 18 that goes through the point (-8, 5), determine the slope of the given line (which is 2) and use the point-slope form of a line to create the equation.
Step-by-step explanation:
To find the equation of a line parallel to y = 2x + 18 that goes through the point (-8, 5), we first need to determine the slope of the given line. The slope of a line in the form y = mx + b is represented by the coefficient of x, which is 2 in this case. Since parallel lines have the same slope, the slope of the line we are looking for is also 2. Now that we have the slope, we can use the point-slope form of a line: y - y1 = m(x - x1), where (x1, y1) is the given point. Plugging in the values (-8, 5) and m = 2, we get y - 5 = 2(x - (-8)). Simplifying, we have y - 5 = 2(x + 8). Expanding, we get y - 5 = 2x + 16. Finally, moving the constant term to the other side, we get the equation of the line parallel to y = 2x + 18 that goes through the point (-8, 5) as y = 2x + 21.