Respuesta :
[tex]\begin{gathered} a)y=-\frac{1}{2}x+\frac{13}{2} \\ b)\frac{1}{2}x+y=\frac{13}{2} \end{gathered}[/tex]
1) We need to rewrite that equation into the Slope-intercept form for a matter of convenience.
[tex]\begin{gathered} x+2y=5 \\ 2y=5-x \\ y=\frac{5-x}{2} \\ y=\frac{5}{2}-\frac{x}{2} \end{gathered}[/tex]2) Now, we can properly work on what was told.
a) Since the point here is to find a parallel equation then we need to keep the same slope. So, our equation must have a slope equal to -1/2
Let's plug point (-3,5) into that:
[tex]\begin{gathered} y=mx+b \\ 5=-\frac{1}{2}(3)+b \\ 5=-\frac{3}{2}+b \\ 5+\frac{3}{2}=b \\ \frac{10}{2}+\frac{3}{2}=b \\ b=\frac{13}{2} \end{gathered}[/tex]Thus, this parallel line that passes through (-3,5) is:
[tex]y=-\frac{1}{2}x+\frac{13}{2}[/tex]b) Let's rewrite it into the Standard form performing some algebraic manipulation adding 1/2x to both sides:
[tex]\frac{1}{2}x+y=\frac{13}{2}[/tex]And those are the answers
