Final answer:
The equation of a line parallel to line 1 with the equation y=-9 and passing through the point (5,5) is y=5. This is because parallel lines have the same slope, which in this case is 0, resulting in a horizontal line.
Step-by-step explanation:
To find the equation of a line parallel to line 1, which has an equation y = -9, and that passes through the point (5,5), we must understand that parallel lines have the same slope. The equation y = -9 represents a horizontal line with a slope of 0. Thus, any line that is parallel to it will also have a slope of 0. The equation of the line we seek must maintain this slope and pass through the given point.
The general form of a linear equation in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Since the slope of our required line is 0, we can write the equation as y = 0x + b, which simplifies to y = b. To find b, we plug in the coordinates of the given point, yielding 5 = 0(5) + b, and solving for b gives us b = 5. Thus, the equation of our line is y = 5.