How do you write the equation of the line that passes through the point (1,4) and is parallel to the line 4x+5y=21?

1 Answer
Aug 27, 2017

Here's the quick and easy way...


Every line parallel to that one has the same slope.
The slope is determined by the ratio of the coefficients of x and y.
If we keep the left side the same, we'll have a parallel line.
what to put on the right?
Using #(1,4)#, we let x = 1 and y = 4.
#4(1) + 5(4) = 4 + 20 = 24#.

Therefore, the line
#4x + 5y = 24#
is parallel to the original and passes through (1, 4).