Answer:
The answer is
[tex]y = \frac{1}{4} x + 4[/tex]
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line.
The equation is
y = 1/4x + 6
Comparing with the general equation above
Slope = 1/4
Since the lines are parallel their slope are also the same
That's
Slope of parallel line = 1/4
So the equation of the parallel line using point (-4 , 3) and slope 1/4 is
[tex]y - 3 = \frac{1}{4} (x + 4) \\ y - 3 = \frac{1}{4} x + 1 \\ y = \frac{1}{4} x + 1 + 3[/tex]
We have the final answer as
[tex]y = \frac{1}{4} x + 4[/tex]
Hope this helps you
