Question

The equation for line A is y=1/3x+4 suppose line A is parallel to line B and point (-3,1) lies on line B select the equation which represents line B in slope intercept form

Answer 1

As given by the question

There are given that the equation of line A is:

$y=\frac{1}{3}x+4$

Now,

From the given equation, the value of slope is:

$m=\frac{1}{3}$

Parallel lines have equal slope, thus

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

The above equation is the line B.

So,

To find the c, substitute the given point (-3, 1) into the partial equation of B

Then,

$\begin{gathered} y=\frac{1}{3}x+c \\ 1=\frac{1}{3}\times(-3)+c \\ 1=-1+c \\ c=2 \end{gathered}$

Then

Put the value of c into the above equation

$\begin{gathered} y=\frac{1}{3}x+c \\ y=\frac{1}{3}x+2 \end{gathered}$

So, the above equation is the equation of line B.

Hence, option D is correct.