Final answer:
The standard form of the equation of a line parallel to y=5/4x+5 and passing through the point (3,3) is -5x + 4y = -3. This is determined by using the slope from the given line and plugging the point into the point-slope form of a line's equation.
Step-by-step explanation:
To write the standard form of the equation of a line that passes through the point (3,3) and is parallel to another line given by the equation y=5/4x+5, we need to use the fact that parallel lines have the same slope. The given line's slope is 5/4; thus, our new line will also have this slope. The standard form of a line's equation is Ax + By = C.
Since the new line must pass through the point (3,3), we can use the point-slope form first: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Plugging our values in gives us: y - 3 = (5/4)(x - 3). Simplify this to get y = (5/4)x - 15/4 + 12/4, which simplifies further to y = (5/4)x - 3/4.
To convert this to standard form, we multiply every term by 4 to eliminate the fractions: 4y = 5x - 3. Then, we rearrange to get -5x + 4y = -3, which is the standard form of our line's equation.