Question

What is the equation of the line perpendicular to the line y=4/9x-2 that passes through the point (4,3)?

Answer 1

y - y₁ = m(x - x₁)
y - 3 = -2¹/₄(x - 4)
y - 3 = -2¹/₄(x) + 2¹/₄(4)
y - 3 = -2¹/₄x - 9
+ 3 + 3
y = -2¹/₄x - 6

Answer 2

The equation of line is
`y=-(9)/(4)x+12`

Explanation:

We have been given the equation of line as
`y=(4)/(9)x-2`

Comparing this equation with the slope intercept form of a line y = mx+b , we get

`m=(4)/(9)\\\\ b=-2`

We know that the slopes of two perpendicular lines are negative reciprocal of each other.

Therefore, the slope of the required line is

`m=-(1)/(4/9) =-(9)/(4)`

Now, this line passes through the point (4,3)

Hence, using the point slope form of the line, the required equation is

`y-y_1=m(x-x_1)\\\\y-3=-(9)/(4) (x-4)\\\\y=-(9)/(4)x+12`

Therefore, the equation of line is

`y=-(9)/(4)x+12`