Answer:
[tex]y=-\frac{5}{3}x-\frac{16}{3}[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
- Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
- Perpendicular lines always have slopes that are negative reciprocals (ex. 2 and -1/2, 4/3 and -3/4, etc.)
1) Determine the slope (m)
[tex]y=\frac{3}{5} x +2[/tex]
From the given equation, we can see that [tex]\frac{3}{5}[/tex] is the slope of the line since it's in the place of m. Because perpendicular lines always have slopes that are negative reciprocals, the line we're currently solving for would have a slope of [tex]-\frac{5}{3}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-\frac{5}{3}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-\frac{5}{3}x+b[/tex]
Plug in the given point (-5,3)
[tex]3=-\frac{5}{3}(-5)+b\\3=\frac{25}{3}+b[/tex]
Subtract [tex]\frac{25}{3}[/tex] from both sides to isolate b
[tex]3-\frac{25}{3}=\frac{25}{3}+b-\frac{25}{3}\\-\frac{16}{3} = b[/tex]
Therefore, the y-intercept is [tex]-\frac{16}{3}[/tex]. Plug this back into [tex]y=-\frac{5}{3}x+b[/tex]
[tex]y=-\frac{5}{3}x+(-\frac{16}{3})\\y=-\frac{5}{3}x-\frac{16}{3}[/tex]
I hope this helps!
