contestada

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

Respuesta :

Panoyin
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:

The equation of line is [tex]y=-\frac{9}{4}x+12[/tex]

Step-by-step explanation:

We have been given the equation of line as [tex]y=\frac{4}{9}x-2[/tex]

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

[tex]m=\frac{4}{9}\\\\ b=-2[/tex]

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

Therefore, the slope of the required line is

[tex]m=-\frac{1}{4/9} =-\frac{9}{4}[/tex]

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

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

[tex]y-y_1=m(x-x_1)\\\\y-3=-\frac{9}{4} (x-4)\\\\y=-\frac{9}{4}x+12[/tex]

Therefore, the equation of line is

[tex]y=-\frac{9}{4}x+12[/tex]