Question

write an equation in slope intercept form form for the line that passes through (-3,5) and is perpendiculat to the graph of the line y=1/3x+4

Answer 1

We will solve as follows:

*First we will determine the slope of the new line:

From theorem we have that two perpendicular lines follow this rule:

$m_1=-\frac{1}{m_2}$

So, the slope of the new line is:

$m=-\frac{1}{(\frac{1}{3})}\Rightarrow m=-3$

*Second, we replace the values of the point and the slope in the following expression:

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

That is:

$y-5=-3(x+3)$

Now, we solve for y:

$y-5=-3x-9\Rightarrow y=-3x-4$

So the equation of the line that fulfills the parameters is:

$y=-3x-4$