Respuesta :
parallel
y=2x+11
Explanation
Step 1
find the equation of the line:
two lines are parellel if the slope is the same for both,so
let
[tex]y_1=2x+6[/tex]this function is written in slope-intercept form y=mx+b, where m is the slope
[tex]\begin{gathered} y=2x+6\rightarrow y=mx+b \\ \text{hence} \\ slope_1=m_1=2 \\ so \\ slope_1=slope_2=m_2=2 \end{gathered}[/tex]it means the slope of the line we are looking for is 2
Step 2
now,let's find the equation of the line
to do that, we can use this formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where m is the slope} \\ \text{and (x}_1,y_1)\text{ is a point from the line} \end{gathered}[/tex]then,let
[tex]\begin{gathered} \text{slope}=2 \\ \text{passing point=(-3,5)} \end{gathered}[/tex]Now,replace in the formula and solve for y
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-5=2(x-(-3)) \\ y-5=2(x+3) \\ y-5=2x+6 \\ \text{add 5 in both sides} \\ y-5+5=2x+6+5 \\ y=2x+11 \end{gathered}[/tex]so, the answer is
[tex]y=2x+11[/tex]I hope this helps you
