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

Answer:

The equation of line is $y=-\frac{9}{4}x+12$

Step-by-step explanation:

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

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

$m=\frac{4}{9}\\\\ b=-2$

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

Therefore, the slope of the required line is

$m=-\frac{1}{4/9} =-\frac{9}{4}$

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

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

$y-y_1=m(x-x_1)\\\\y-3=-\frac{9}{4} (x-4)\\\\y=-\frac{9}{4}x+12$

Therefore, the equation of line is

$y=-\frac{9}{4}x+12$

Answer 2

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