Write the equation in standard form line through (2,5) parallel to y=-4/5x+1
To find the standard form of the equation for a line parallel to the given line and passing through the point (2,5), we first need to determine the slope of the line parallel to y = -4/5x + 1.
The given line is in slope-intercept form y = mx + b, where m represents the slope. In this case, the slope is -4/5.
Since the slope of parallel lines is equal, the slope of the line we are trying to find is also -4/5.
Using the point-slope form, y - y1 = m(x - x1), where (x1, y1) represents the coordinates of the point, we can substitute the slope m and the coordinates (2,5).
y - 5 = -4/5(x - 2)
Multiplying through by 5 to eliminate the fraction:
5y - 25 = -4(x - 2)
Expanding the expression:
5y - 25 = -4x + 8
Rearranging the equation to put it in standard form (Ax + By = C):
4x + 5y = 33
Therefore, the equation of the line in standard form passing through the point (2,5) and parallel to y = -4/5x + 1 is 4x + 5y = 33.