Question

Write the equation of a line perpendicular to y=-12x+2 going through (0,-1)

Answer 1

             $\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}$

          Write the equation of a line perpendicular to y=-12x+2 going

           through (0, -1)

     $\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}$

        First, let's take a look at our provided information:-

• A line $\text{y=-12x+2}$
• A point (0, -1)
• The line $\text{y=-12x+2}$ is perpendicular to the line that goes through (0, -1)

     If two lines are perpendicular to each other, their slopes are opposite reciprocals of each other.

   So we take the slope of the given line, which is -12, change its sign from minus to plus:-

$\Large\textit{12}$

And now, We flip the number over:-

$\Large\displaystyle\frac{1}{12}$

Now that we've found the slope of the line, let's find its equation.

     The first step is to write it in point-slope form as follows:-

$\longmapsto\sf{y-y_1=m(x-x_1)}$

Replace letters with numbers,

$\longmapsto\sf{y-(-1)=\displaystyle\frac{1}{12}(x-0)}$

On simplification,

$\longmapsto\sf{y+1=\displaystyle\frac{1}{12} (x-0)}$

On further simplification,

$\longmapsto\sf{y+1=\displaystyle\frac{1}{12} x}$

Subtracting 1 on both sides,

$\longmapsto\sf{y=\displaystyle\frac{1}{12} x-1}$

$\Uparrow\texttt{Our equation in slope-intercept form}$

Good luck with your studies.

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