Write the equation 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
To write the equation of a line in standard form, we need to rearrange the equation so that the coefficients of x and y are both positive integers.
The given equation is y = -4/5x + 1.
To find the equation of a line parallel to this, we know that parallel lines have the same slope. Therefore, the slope of the new line is also -4/5.
Using the point-slope form of a line, we can write the equation as:
y - y1 = m(x - x1)
where (x1, y1) is the given point (2, 5) and m is the slope (-4/5).
Plugging these values into the equation, we get:
y - 5 = (-4/5)(x - 2)
Multiplying both sides by 5 to eliminate the fraction:
5(y - 5) = -4(x - 2)
Expanding both sides:
5y - 25 = -4x + 8
Rearranging the equation to be in standard form:
4x + 5y = 33
Therefore, the equation of the line through (2, 5) parallel to y = -4/5x + 1 is option D: 4x - 5y = 33.