Question

Find an equation of the line that passes through (3, 1) and it’s parallel to the line y = 1/3x+6

Answer 1

Given the equation of the line: y = 1/3 x+6

And the point (3, 1)

The required line is parallel to the given line

So, the slopes of the line are equal

the slope of the given line = 1/3

So, the slope of the required line = m = 1/3

The general equation will be:

$y=\frac{1}{3}x+b$

We will find the value of (b) using the point (3, 1)

when x = 3, y = 1

Substitute into the equation and solve for (b)

$\begin{gathered} 1=\frac{1}{3}\cdot3+b \\ 1=1+b \\ b=1-1=0 \end{gathered}$

So, the answer will be the equation of the line:

$y=\frac{1}{3}x$