Perpendicular Lines
When a line is perpendicular, it means that their slope is the negative reciprocal of the reference line.
Examples of negative reciprocals:
1/3 and -3
-4/7 and 7/4
Solving the Question
We're given:
- [tex]y=\dfrac{9}{5}x-2[/tex]
- Passes through (5,–3)
Slope intercept form: [tex]y=mx+b[/tex]
Finding the slope
We know that the slope of the line will be the negative reciprocal of [tex]\dfrac{9}{5}[/tex]:
[tex]-\dfrac{5}{9}[/tex]
⇒ Plug this into y=mx+b:
[tex]y=-\dfrac{5}{9}x+b[/tex]
Finding the y-intercept
To find the y-intercept, plug in the given point and solve for b:
[tex]-3=-\dfrac{5}{9}*5+b\\\\-3=-\dfrac{25}{9}+b\\\\b=-\dfrac{2}{9}[/tex]
⇒ Plug this into our equation:
[tex]y=-\dfrac{5}{9}x-\dfrac{2}{9}[/tex]
Answer
[tex]y=-\dfrac{5}{9}x-\dfrac{2}{9}[/tex]
