Answer:
equation of the parallel line will be [tex]y=\frac{1}{3}x+3[/tex].
Step-by-step explanation:
If the two lines have been given as y = mx + c
and y = m'x + c'
Where m and m' are the slopes of the given lines.
If these lines are parallel to each other then slopes of the lines will be same (m = m').
Equation of the given line is y = [tex]\frac{1}{3}x+4[/tex] with he slope = [tex]\frac{1}{3}[/tex]
Then slope of a line parallel to this line m = [tex]\frac{1}{3}[/tex]
Equation of the parallel line will be [tex]y=\frac{1}{3}x+c[/tex]
Since the line passes through a point (6, 5)
Then [tex]5=\frac{1}{3}\times (6)+c[/tex]
5 = 2 + c
c = 5 - 2
c = 3
Therefore, equation of the parallel line will be [tex]y=\frac{1}{3}x+3[/tex]
