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Write the standard form of the equation of the line described. a) through (1,1) , parallel to y= -3x-1

Write the standard form of the equation of the line described. a) through (1,1) , parallel-example-1
User Leolobato
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Concept: We were told that the point (1,1) is parallel to y = -3x - 1

Let us obtain our slope from the equation given

The general form of equation of line is written in the form


\begin{gathered} y=mx+c \\ \\ where,m=slope \end{gathered}

Therefore,


\begin{gathered} y=-3x-1 \\ \therefore m=-3 \end{gathered}

Since, the point is parallel to the line given. Therefore, the slope is the same.

The formula for the equation of the line given one point is,


y-y_1=m(x-x_1)

Thus


\begin{gathered} y-1=-3(x-1) \\ y-1=-3x+3 \\ y=-3x+3+1 \\ y=-3x+4 \end{gathered}

Hence, the equation in its standard form is


\begin{gathered} 3x+y=4 \\ \end{gathered}

User IncredibleHat
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