Answer:
[tex]y=\frac{1}{2} x-8[/tex]
Step-by-step explanation:
The final answer is in the slope-intercept form, which is y=mx +c, where m is the slope and c is the y-intercept.
The slope of a perpendicular line is the negative reciprocal of the slope of the given line (the line it is perpendicular to). Thus, let's find the slope of the given line first.
Given line: y= -2x -9
The above equation is already in the slope-intercept from and thus, the slope is the coefficient of x.
Slope of given line= -2
The coefficient is the number that comes before a variable and it includes the positive or negative sign, which explains why the slope of the given line is -2 instead of 2.
Slope of perpendicular line= [tex]\frac{1}{2}[/tex]
Substitute the value of the slope into the equation:
[tex]y=\frac{1}{2} x+c[/tex]
To find the value of c, substitute a pair of coordiantes the line passes through.
When x= 8, y= -4,
[tex]-4=\frac{1}{2}(8)+c[/tex]
-4= 4 +c
c= -4 -4
c= -8
Thus, the equation of the perpendicular line is [tex]\bf{y=\frac{1}{2} x-8}[/tex].
What is reciprocal?
- The reciprocal of a number is 1 divided by that number
- For example, the reciprocal of 2 is [tex]\frac{1}{2}[/tex]
- In this question, we are interested in negative reciprocal. This means that if the slope of the given line is m, the slope of the perpendicular line is [tex]-\frac{1}{m}[/tex].
