# 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?

Aug 27, 2017

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 $\left(1 , 4\right)$, we let x = 1 and y = 4.
$4 \left(1\right) + 5 \left(4\right) = 4 + 20 = 24$.

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