Final answer:
To find the equation of a line parallel to y = 5x − 9 that passes through (5, 27), we use the point-slope form with the slope of 5 resulting in the standard form of the equation 5x − y − 2 = 0.
Step-by-step explanation:
To write an equation of a line in standard form with integer coefficients that passes through the point (5, 27) and is parallel to the line given by the equation y = 5x − 9, we first note that parallel lines have the same slope. Thus, the slope of our new line is the same as the given line, which is 5. Now let's use the point-slope form of a line equation, which is y − y1 = m(x − x1), where (x1, y1) is the point the line passes through and m is the slope. Substituting the point (5, 27) and the slope 5 into this equation gives us y − 27 = 5(x − 5). Expanding this: y − 27 = 5x − 25 and then bringing all terms to one side gives us 5x − y − 2 = 0. This is the equation of our line in standard form with integer coefficients.