what is the slope of a line perpendicular to 6x-3y=6?

Question

 i need help with a question about perpendicular lines and slopes. thank you!

Answer 1

The standard form of a line looks like:  Ax + By = C

 

Now, just once, and forever, convert this to the slope-intercept form:  y = mx + b

                                                     y = (-A/B)x + C/B

 

That means that if you have the equation of a line in standard form, you may immediately read both the slope and the y-intercept (and also the x-intercept) from it.

 

The slope of the line with equation    6x - 3y =6     or     2x - y = 2    (reduced)

                                                                                is  (-2/(-1)) = 2

The perpendicular line has a slope of:  -1/2

 

Save yourself pages of math equations over a lifetime and memorize this.  The Standard Form of a line has many advantages.

                                                     

Answer 2

Before dealing with any information specific to this question, remember that two lines are perpendicular when their slopes are negative reciprocals. That means that if one line has a slope m, the other line must have a slope of -1/m. 

 

We want to arrange the given line equation into y=mx+b form, so we can just read the slope right away.

6x-3y=6

move 6x to the other side

-3y=-6x+6

divide all terms by -3

(-3/-3)y=(-6/-3)x+(6/-3)

simplify

y=2x-2 = mx+b

 

The slope for this line is m=2. The perpendicular slope is -1/2.

 

 

Answer 3

6x-3y=6

-3y=-6x+6

multiply both sides by -1

3y=6x-6

divide both sides by 3

y=2x-2

the slope of this line is 2 or 2/1 (y=mx+b where m=slope)

the slope of a line that is perpendicular to this line will be the negative reciprocal of 2/1

the negative reciprocal of 2/1 is -1/2 or -(1/2)