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Sagot :
[tex]y=-4x+13[/tex]
Explanation
two lines are parallel when their slopes are equal,
Step 1
convert the equation to the form
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope} \end{gathered}[/tex]to easily find m
[tex]\begin{gathered} 4x+3y=15 \\ \text{subtract 4x in both sides} \\ 4x+3y-4x=15-4x \\ 3y=15-4x \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{15}{3}-4x \\ y=-4x+5 \end{gathered}[/tex]Hence
[tex]\begin{gathered} y=-4x+5\Rightarrow y=mx+b \\ m=\text{slope}=-4 \end{gathered}[/tex]Step 2
Now we have this info to find the equation of the line
[tex]\begin{gathered} P1(3,1) \\ m_1=m_2=-4 \end{gathered}[/tex]apply the formula
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{replacing} \\ y-1=-4(x-3) \\ y-1=-4x+12 \\ \text{add 1 in both sides} \\ y-1+1=-4x+12+1 \\ y=-4x+13 \end{gathered}[/tex]I hope this helps you
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