Given:
The equation of the line is
[tex]y=x-3[/tex]
Required:
Find the equation of the line that is parallel to the given line and contains the point (3,-2).
Explanation:
The given equation of the line is
[tex]y=x-3[/tex]
Compare the equation with the equation
[tex]y=mx+c[/tex]
The slope of the line m = 1.
Since the slope of the parallel lines is equal.
The equation of the line that is parallel to the given line is:
[tex]y=x+b[/tex]
This line contains the point (3,-2).
[tex]\begin{gathered} -2=3+b \\ b=-5 \end{gathered}[/tex]
Thus the equation of the parallel line is:
[tex]y=x-5[/tex]
Final Answer:
[tex][/tex]
