Final answer:
To find the equation of a line parallel to y = -3x + 7 that passes through (3,5), maintain the same slope of -3 and apply the point-slope form to get y = -3x + 14, which is the desired equation.
Step-by-step explanation:
First, we identify the slope of the given line, which is -3.
Since parallel lines have equal slopes, our new line will also have a slope of -3.
We then use the point-slope form, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through.
Plugging in our slope and point values we get: y - 5 = -3(x - 3).
To put this into slope-intercept form, we simplify the equation:
- y - 5 = -3x + 9 (distribute the -3 into the parentheses)
- y = -3x + 9 + 5 (add 5 to both sides to isolate y)
- y = -3x + 14 (combine like terms)
Therefore, the equation of the line parallel to y = -3x + 7 that passes through the point (3,5) is y = -3x + 14.