Question

ASAP! What is the y intercept of the line perpendicular to the line y = 4/3x + 1 that includes the point (4, 1)?

Answer 1

y-intercept is 4.

Explanation:

Given,

Equation of the line,

`y=(4)/(3)x+1`

∵ Equation of a line is y = mx + c, where m is the slope of the line,

By comparing,

The slope of the above line is
`(4)/(3)`,

Let m' is the slope of the line perpendicular to above line,

`\implies m'* (4)/(3)=-1`

`\implies m' = -(3)/(4)`

Now, the equation of a line passes through a point
`(x_1,y_1)` is,

`y-y_1=m(x-x_1)`

So, the equation of the perpendicular line having slope
`-(3)/(4)` and passes through ( 4,1) is,

`y-1=-(3)/(4)(x-4)\implies y=-(3)/(4)x+3+1\implies y=-(3)/(4)x+4`

For y-intercept,

x = 0,

⇒ y = 4

Hence, the y-intercept of the perpendicular line is 4.