The equation that represents the line that perpendicular to the graph of 4x+3y=9and pases through (-2,3) is y = (3/4)*x + 4.5
How to find the perpendicular equation?
Two lines:
y = ax + b
y = mx + c
Are perpendicular only if the product between the slopes is -1, so:
a*m = -1
The given equation is:
4x + 3y = 9
Solving for y, we get:
3y = -4x + 9
y = (-4/3)*x + 3
The slope of the perpendicular line is a, such that:
a*(-4/3) = -1
a = 3/4
So our line is:
y = (3/4)*x + b
We know that this line passes through (-2, 3), then we will get:
3 = (3/4)*-2 + b
3 + 3/2 = b
4.5 = b
The linear equation is:
y = (3/4)*x + 4.5