# How do you write an equation of the line containing the point (4, 6) and the parallel to the line y= 1/4x + 4?

Apr 23, 2018

$y = \frac{1}{4} x + 5$

#### Explanation:

The formula for finding the equation of a line:

y- (y_1 \ "from the coordinate") = "gradient"(x-(x_1 \ "from the coordinate"))

So applying that formula

$y - 6 = \frac{1}{4} \left(x - 4\right)$

$y - 6 = \frac{1}{4} x - 1$

$y = \frac{1}{4} x + 5$

The gradient is $\frac{1}{4}$ because parallel lines have the same gradient.