Answer : Equation of line is y=Equation of line is y=[tex]\frac{2}{3}[/tex]x+[tex]\frac{-5}{3}[/tex]
Step-by-step explanation:
Theory :
Equation of line is given as y = mx + c.
Where, m is slope and c is y intercepted.
Slope of given line : y = [tex]\frac{2}{3}[/tex]x+1 is m= [tex]\frac{2}{3}[/tex]
We know that line : y = [tex]\frac{2}{3}[/tex]x+1 is parallel to equation of target line.
therefore, slope of target line will be [tex]\frac{2}{3}[/tex].
we write equation of target line as y= [tex]\frac{2}{3}[/tex]x+c
Now, It is given that target line passes through point ( -5,-2)
hence, point ( -5,-2) satisfy the target line's equation.
we get,
y= [tex]\frac{2}{3}[/tex]x+c
-2= [tex]\frac{2}{3}[/tex] [tex]\times[/tex] -5+ c
-5= [tex]\frac{-10}{3}[/tex]+c
c= [tex]\frac{-5}{3}[/tex]
thus, Equation of line is y=Equation of line is y=[tex]\frac{2}{3}[/tex]x+[tex]\frac{-5}{3}[/tex]
