Question

What is the equation of a line that is perpendicular to y - 3x-2 and passesthrough the point (6,8)?yyO A. --****O B. --*x+10O C. --***O D. x-x+6y-

Answer 1

The given equation is of the form y = mx + b, where m is the slope and b is the y-intercept.

So in the equation y = 3x - 2, the slope is 3.

And we know that perpendicular lines have opposite reciprocal slopes. So the slope of the line you want is:

`m=(-1)/(3)=-(1)/(3)`

Next, we have the point (6,8). So, Use the slope-intercept form of a line to substitute those values and write your new equation:

`\begin{gathered} y=mx+b \\ 8=(-(1)/(3))(6)+b \\ 8=-2+b \\ 8+2=-2+b+2 \\ b=10 \end{gathered}`

The new equation is:

`y=-(1)/(3)x+10`

Answer: B.