Question

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?

Answer 1

Here's the quick and easy way...

Explanation:

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.
So...
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).