Write an equation of a line containing (2, - 3) and perpendicular to 3x + 4y = 14.

To solve this, we first have to find out what the slope of 3x + 4y = 14

To do this, we solve for y, and use the equation y = mx + b (m = slope)

3x + 4y = 14

4y = - 3x + 14

y = - 3/4x + 14/4

So - 3/4 is the slope of the line.

But! We need to use the perpendicular version of this slope, which is 4/3

So now we use 4/3 in y = mx + b to find b

-3 = 4/3 (2) + b

-3 = 8/3 + b

-8/3 - 9/3 = b

-17/3 = b

So our final equation is:

y = 4/3x - 17/3