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=-(1)/(m_2)`

So, the slope of the new line is:

`m=-(1)/(((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`