What is the equation of the line perpendicular to 7x − 2y = −24 that contains the point (14, −2)?

First, you have to change the equation given into point-slope form.

-2y=-7x-24
2y=7x+24
y=7y/2 + 12

A line perpendicular to this one would have an opposite reciprocal for the slope value. This means that the slope of the perpendicular line would be -2/7.

Now we can put the values into the basic equation.

y=-2/7x + b

Substitute the values for the points to find the y-intercept.
-2= -2/7(14) + b
-2= -28/7 +b
-2= -4 + b
b=2

Now that we have the intercept, we can pull together our final equation.
y= -2x/7 + 2