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Write an equation in slope-intercept form for the line that passes through (-1,4) and perpendicular to the line y=3x+5

User Skoperst
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The line is perpendicular to the equation:


y=3x+5

So our slope will be the negative reciprocal of the slope of this line so the new slope will be:


m=-(1)/(3)

Now with the slope we can find the intercept in the y axis with the slope equation:


m=(y-y_1)/(x-x_1)

So we replace the slope and the coordinate, and replace x=0 to find the intercept so:


\begin{gathered} -(1)/(3)=(y-4)/(0-(-1)) \\ y-4=-(1)/(3) \\ y=4-(1)/(3) \\ y=(11)/(3) \end{gathered}

So the general equation will be:


y=-(1)/(3)x+(11)/(3)

User Bernesto
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