Answer:
[tex]y=-\dfrac{1}{3}x-1[/tex]
Step-by-step explanation:
Given:
line y=3x-1
point (-3,0)
Write: equation of the line that is perpendicular to the given and passes through the point (-3,0)
Solution:
The slope of the given line is [tex]m=3[/tex]
If [tex]m_1[/tex] is the slope of perpendicular line, then
[tex]m\cdot m_1=-1\\ \\3m_1=-1\\ \\m_1=-\dfrac{1}{3}[/tex]
So, the equation of the needed line is [tex]y=-\dfrac{1}{3}x+b.[/tex]
Find b. This line passes through the point (-3,0), so its coordinates satisfy the equation:
[tex]0=-\dfrac{1}{3}\cdot (-3)+b\\ \\0=1+b\\ \\b=-1\\ \\y=-\dfrac{1}{3}x-1[/tex]
