What is the equation of a line that is perpendicular to y = 3 x − 2 and passes through the point ( 6 , 8 ) was

Hello!

To find the line that is perpendicular to y = 3x - 2 and passes through the ordered pair (6, 8), we will:

Let's remind ourselves of slope-intercept formula. Slope-intercept formula is y = mx + b, where m is the slope, and b is the y-intercept.

In the given equation, we know that 3 is slope. With that, we can find the negative reciprocal of that slope, and continue to step #2.

To find the reciprocal, we will need to flip our fraction. In this case, 3/1 = 3, so once we flip it, it is 1/3. Since it is the negative reciprocal, the fraction is a negative, so the negative reciprocal is -1/3.

Now, we will substitute the ordered pair into the slope-intercept formula with our new slope.

y = -1/3x + b (6, 8)

8 = -1/3(6) + b

8 = -2 + b (add 2 to both sides)

10 = b

Therefore, the equation of the line is y = -1/3x + 10.