Question

What is the y-intercept of the line perpendicular to the line y = 3x + 3 that includes the point (3, 1)?

Answer 1

Given:

The line perpendicular to the line y = 3x + 3 includes the point (3, 1).

Required:

We need to find the line equation.

Step-by-step explanation:

The given line y =3x+3 is of the form.

`y=m_1x+b`
`where\text{ slope,}m_1=3\text{ and b=3.}`

The slope of the line is a negative reciprocal of the perpendicular to the line.

`m=negative\text{ reciprocal of }m_1`
`m=-(1)/(3)`

Consider the line equation.

`y=mx+b`

Substitute m=-1/3 in the equation.

`y=-(1)/(3)x+b`

Substitute x =3 and y =1 in the equation to find the value of b.

`1=-(1)/(3)(3)+b`

`1=-1+b`

Add 1 to both sides of the equation.

`1+1=-1+b+1`
`2=b`

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.