Question

What is an equation of the line that passes through the point (3,1) and is parallelto the line 4x + 3y=15

Answer 1

$y=-4x+13$

Explanation

two lines are parallel when their slopes are equal,

Step 1

convert the equation to the form

$\begin{gathered} y=mx+b \\ \text{where m is the slope} \end{gathered}$

to easily find m

$\begin{gathered} 4x+3y=15 \\ \text{subtract 4x in both sides} \\ 4x+3y-4x=15-4x \\ 3y=15-4x \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{15}{3}-4x \\ y=-4x+5 \end{gathered}$

Hence

$\begin{gathered} y=-4x+5\Rightarrow y=mx+b \\ m=\text{slope}=-4 \end{gathered}$

Step 2

Now we have this info to find the equation of the line

$\begin{gathered} P1(3,1) \\ m_1=m_2=-4 \end{gathered}$

apply the formula

$\begin{gathered} y-y_1=m(x-x_1) \\ \text{replacing} \\ y-1=-4(x-3) \\ y-1=-4x+12 \\ \text{add 1 in both sides} \\ y-1+1=-4x+12+1 \\ y=-4x+13 \end{gathered}$

I hope this helps you