Write the equation of the line in standard form the line through (2,5) parallel to y=-4/5x+1
A. 5x+4y=-33
B. 4x+5y=-33
C. 4x+5y=33
D. 4x-5y=33
The slope of a line parallel to another line is the same. Since the given line has a slope of -4/5, the line parallel to it will also have a slope of -4/5. Using the point-slope form of a line, we can write the equation:
y - y₁ = m(x - x₁),
where (x₁, y₁) = (2, 5) and m = -4/5. Substituting these values into the equation, we get:
y - 5 = -4/5(x - 2).
Expanding and rearranging the equation, we have:
5y - 25 = -4x + 8
4x + 5y = 33.
Therefore, the equation of the line in standard form is 4x + 5y = 33. The answer is option C.