Question

What is the y-intercept of the line perpendicular to the line Y= -3/4 x + 5 that includes the point (-3,-3?

Answer 1

The y intercept is at y = 1

Explanation:

Step 1 :

Given, line's equation is = Y= -
`(3)/(4)` x + 5

Slope of the line perpendicular to this line =
`(4)/(3)` [As the product of the slope of 2 perpendicular lines is -1]

The point (-3,-3) lies on the line

Hence the new line's equation can be obtained using the formula

(y - y1 ) = m (x-x1) ,

where (x1,y1) = point on the line

m = slope of the line

Substituting,

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

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

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

Step 2 :

To find the y intercept.

At the point of y - intercept, that is when the line touches the y axis, the x co ordinate = 0

So substituting x = 0 in the line's equation, we have

y = 0 + 1 = 1

y = 1

Step 3 :

Answer :

The y intercept is at y = 1