Answer:
[tex]y=\frac{2}{3}x+\frac{7}{3}[/tex]
Step-by-step explanation:
step 1
Find the slope of the line parallel to the given line
we know that
If two lines are parallel, then their slopes are equal
we have
[tex]y=\frac{2}{3}x-4[/tex] ---> given line
The slope of the given line is [tex]m=\frac{2}{3}[/tex]
so
the slope of the line parallel to the given line is [tex]m=\frac{2}{3}[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{2}{3}[/tex]
[tex]point\ (4,5)[/tex]
substitute
[tex]y-5=\frac{2}{3}(x-4)[/tex]
step 3
Convert to slope intercept form
[tex]y=mx+b[/tex]
isolate the variable y
[tex]y-5=\frac{2}{3}x-\frac{8}{3}[/tex]
[tex]y=\frac{2}{3}x-\frac{8}{3}+5[/tex]
[tex]y=\frac{2}{3}x+\frac{7}{3}[/tex]
