Final answer:
To find an equation for a line parallel to the given line that contains point C(1,5), we need to find the slope of the given line and use the point-slope formula.
Step-by-step explanation:
To find an equation for a line parallel to the given line that contains point C(1,5), we need to find the slope of the given line. The equation of the given line is y = (1/9)x + 5, which is in the form y = mx + b, where m is the slope. So, the slope of the given line is 1/9.
Since parallel lines have the same slope, the equation of the line parallel to the given line will also have a slope of 1/9. We can now use the point-slope form of a linear equation to write the equation of the line parallel to the given line:
y - y1 = m(x - x1)
Substituting the values of C(1,5) and m = 1/9 into the equation, we get:
y - 5 = (1/9)(x - 1)
This is the equation of the line parallel to the given line that contains point C(1,5).