Answer:
\(y+3=\frac{5}{3}(x-9)\) or \(y=\frac{5}{3}x-18\)
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 the same
we have
\(y=\frac{5}{3}x-4\)
therefore
The slope m of the line parallel to the given line is
\(m=\frac{5}{3}\)
step 2
Find the equation of the line in point slope form
\(y-y1=m(x-x1)\)
we have
\(m=\frac{5}{3}\)
\(point\ (9,-3)\)
substitute
\(y+3=\frac{5}{3}(x-9)\) ----> equation of the line in point slope form
step 3
Find the equation of the line in slope intercept form
\(y=mx+b\)
we have
\(y+3=\frac{5}{3}(x-9)\)
Isolate the variable y
\(y+3=\frac{5}{3}x-15\)
\(y=\frac{5}{3}x-15-3\)
\(y=\frac{5}{3}x-18\)
