Answer:
y=-4/3x-10
Explanation:
To find the equation of a line perpendicular to y=3/4x+9 and passing through the point (3, -14), we'll use the fact that the slopes of perpendicular lines are negative reciprocals.
The given line has a slope of 3/4 The negative reciprocal of 3/4 is -4/3 so the slope of the perpendicular line is -4/3
Now we can use point-slope form of a linear equation
y-y1=m(x-x1)
were
m= slope
(x1,Y1) = point on line
in this case m= -4/3 and x1,y1 = (3,-14)
y-(-14)=-4/3(x-3)
simplify
y+14=-4/3x+4
Subtract 14 from both sides
y=-4/3x-10
So, the equation of the line perpendicular to y=3/4x+9 and passing through point (3,-14 )is y=-4/3x-10