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

Solution:

Given y = 4/9x - 2 and the point (4,3)

We have a slope intercept form, y = mx + c where m is slope and c is intercept

The slope of given equation is 4/9

We know that the product of slopes of two perpendicular lines is equal to -1.

Let the slope of the required equation be n

⇒ mn = -1

⇒ (4/9)n = -1

⇒ n = -9/4

It is given that the equation passes through (4, 3)

⇒ 3 = (-9/4)(4) + c

⇒ c = 9 + 3 = 12

Therefore, the required equation is y = (-9/4)x + 12

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

Summary:

The equation of the line perpendicular to the line y = 4/9x - 2 that passes through the point (4, 3) is y = (-9/4)x + 12.