Answer:
[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]
Step-by-step explanation:
The slope of a line that is perpendicular to another will have an opposite-reciprocal slope. So, if the slope was -2, then the perpendicular slope would be [tex]\frac{1}{2}[/tex] .
[tex]y=-5x+11[/tex]
This is written in slope-intercept form:
[tex]y=mx+b[/tex]
m is the slope and b is the y-intercept. Find the opposite-reciprocal of the slope, -5:
[tex]y=\frac{1}{5} x+b[/tex]
Now we need to find the y-intercept. For this, substitute the given points for its appropriate value:
[tex](3_{x},3_{y})\\\\3=\frac{1}{5}(3)+b[/tex]
Solve for b:
Simplify multiplication:
[tex]\frac{1}{5}*\frac{3}{1}=\frac{3}{5}[/tex]
Insert:
[tex]3=\frac{3}{5}+b[/tex]
Subtract b from both sides:
[tex]3-b=\frac{3}{5}+b-b\\\\3-b=\frac{3}{5}[/tex]
Subtract 3 from both sides:
[tex]3-3-b=\frac{3}{5}-3\\\\-b=\frac{3}{5}-3[/tex]
Simplify subtraction:
[tex]\frac{3}{5}-3\\\\\frac{3}{5}-\frac{3}{1}\\\\\frac{3}{5}-\frac{15}{5}=-\frac{12}{5}[/tex]
Insert:
[tex]-b=-\frac{12}{5}[/tex]
Multiply both sides by - 1 to simplify b (it can be seen as -1b):
[tex]-b*(-1)=-\frac{12}{5}*(-1)\\\\b=\frac{12}{5}[/tex]
Insert:
[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]
:Done
