Answer:
y = -4x - 4
Step-by-step explanation:
If we have two lines in slope intercept form as
[tex]y = m_1x + c_1 \text{ and}\\y = m_2x + c_2\\[/tex]
then the product of the slopes [tex]m_1m_2 = -1[/tex]
In other words, [tex]m_2 = -\frac{1}{m_1}[/tex]
We have the first line as
[tex]y = \frac{1}{4}x + 5\\\\[/tex]
The slope of this line is [tex]\frac{1}{4}[/tex]
The slope of a perpendicular line will be the negative of the reciprocal of this line
Reciprocal of 1/4 is 4
So slope of perpendicular line is -4 which implies
y = -4x + c
We have to determine c
Since the line passes through (-3, 8), plug in these values for x and y in the equation and solve for c
8 = (-4)(-3) + c
8 = 12 + c
c = -4
So the equation of the perpendicular line is y = -4x - 4 (Answer)
It is always a good idea to plot these graphs and see if they fit the data provided
The attached plot shows the two graphs and you can see they are perpendicular to each other and the perpendicular line(the answer) passes through point (-3,8)
