Question

Consider the following equation

Answer 1

Answer:

The perpendicular line is:

y = 1/3  x + 2/3

Step-by-step explanation:

The given equation can be reduced to its slope-intercept form as shown below:

3x + 9y = 8y - 2

subtract 8 y from both sides

3 x + y = -2

subtract 3 x from both sides

y = - 3 x -2

therefore we know that the slope of this line is -3, and then, a perpendicular line to it must have slope given by the "opposite of the reciprocal" of this slope. That is, the slope of any perpendicular line to this one must be: 1/3

We use this slope to find the equation of the line passing through the point (13. 5)

y = 1/3 x + b

passing through (13, 5) means:

5 = 1/3 (13) + b

therefore, we can find b from the above equation

b = 5 - 13/3 = 15/3 - 13/3 = 2/3

Then the equation of this perpendicular line is:

y = 1/3  x + 2/3