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How do I write the equation of the line passing through (-3, 5) and parallel to the line y = 2x + 6.

User Krasnoff
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1 Answer

2 votes

parallel

y=2x+11

Step-by-step explanation

Step 1

find the equation of the line:

two lines are parellel if the slope is the same for both,so

let


y_1=2x+6

this function is written in slope-intercept form y=mx+b, where m is the slope


\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}

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:


\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}

then,let


\begin{gathered} \text{slope}=2 \\ \text{passing point=(-3,5)} \end{gathered}

Now,replace in the formula and solve for y


\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}

so, the answer is


y=2x+11

I hope this helps you

User Sandeep Kokate
by
9.0k points

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