Answer:
[tex]y=-\frac{1}{3}x+7[/tex]
Step-by-step explanation:
we know that
If two lines are parallel then their slopes are equal
The equation of the given line is
[tex]y=-\frac{1}{3}x+4[/tex]
the slope is [tex]m=-\frac{1}{3}[/tex]
so
the slope of the parallel line to the given line is also [tex]m=-\frac{1}{3}[/tex]
Find the equation of the line that is parallel to the given line and passes through the point (6, 5)
we have
[tex]m=-\frac{1}{3}[/tex]
[tex]point\ (6,5)[/tex]
The equation of the line in point slope form is
[tex]y-y1=m(x-x1)[/tex]
substitute
[tex]y-5=-\frac{1}{3}(x-6)[/tex]
Convert to slope intercept form
[tex]y=mx+b[/tex]
isolate the variable y
[tex]y-5=-\frac{1}{3}x+2[/tex]
[tex]y=-\frac{1}{3}x+2+5[/tex]
[tex]y=-\frac{1}{3}x+7[/tex]
