Answer:
[tex]y = -\frac{1}{3}x + 4[/tex]
Step-by-step explanation:
Required
Equation of line
passes through [tex](6,2)[/tex]
In an equation of the form [tex]y =mx + b[/tex]; the slope is [tex]m[/tex]
So, by comparison;
The slope of [tex]y = 3x + 1[/tex] is: [tex]m =3[/tex]
From the question, we understand that the required equation is perpendicular to [tex]y = 3x + 1[/tex]
This means that its slope is:
[tex]m_2 =-\frac{1}{m}[/tex]
So, we have:
[tex]m_2 =-\frac{1}{3}[/tex]
The line equation is:
[tex]y = m_2(x - x_1) + y_1[/tex]
Where:
[tex](x_1,y_1) = (6,2)[/tex]
So, we have:
[tex]y = -\frac{1}{3}(x - 6) + 2[/tex]
[tex]y = -\frac{1}{3}x + 2 + 2[/tex]
[tex]y = -\frac{1}{3}x + 4[/tex]
