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