Given:
The line perpendicular to the line y = 3x + 3 includes the point (3, 1).
Required:
We need to find the line equation.
Explanation:
The given line y =3x+3 is of the form.
[tex]y=m_1x+b[/tex][tex]where\text{ slope,}m_1=3\text{ and b=3.}[/tex]The slope of the line is a negative reciprocal of the perpendicular to the line.
[tex]m=negative\text{ reciprocal of }m_1[/tex][tex]m=-\frac{1}{3}[/tex]Consider the line equation.
[tex]y=mx+b[/tex]Substitute m=-1/3 in the equation.
[tex]y=-\frac{1}{3}x+b[/tex]Substitute x =3 and y =1 in the equation to find the value of b.
[tex]1=-\frac{1}{3}(3)+b[/tex][tex]1=-1+b[/tex]Add 1 to both sides of the equation.
[tex]1+1=-1+b+1[/tex][tex]2=b[/tex]We know that b is the y-intercept.
Final answer:
The y-intercept of the line perpendicular to the line y = 3x + 3 includes the point (3, 1) is 2.
