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What is the equation of the line perpendicular to 3x+y=6 that passes through the
point (-6, -1)?

What Is The Equation Of The Line Perpendicular To 3xy6 That Passes Through The Point 6 1 class=

Sagot :

BeccaKA

Answer: y = -1/3x - 3

Step-by-step explanation:

First, convert this equation into slope intercept form (y = mx + b where m is the slope and b is the y-intercept)

  • To convert this equation into slope-intercept form, all you have to do is subtract 3x from both sides to give you the equation y = 3x + 6

Next, you need to find the slope of your new equation. The slope of a perpendicular line will have a slope that is the opposite reciprocal of the first slope, which means it will have the opposite sign and the fraction will be flipped (even whole numbers are a fraction - they are divided by 1)

  • Since the slope of the first equation is positive 3, you are going to change the sign to a negative and flip the fraction from 3/1 to 1/3, which gives you a slop of -1/3

Now that you have your slop, you need to find your y-intercept. To do this, you use the point that you are given. In the previous step, you figured out the slope, so now you can enter that into your new equation. Then, plug the x-coordinate in for x and the y-coordinate in for y in the equation.

  • At this point, your equation is y = -1/3x + b. You can plug -6 in for x and -1 in for y to give you the equation -1 = -1/3(-6) + b

The next step is to solve the equation like you would any other equation.

  • Multiply -6 by -1/3 to get 2, then subtract 2 from -1 to get b = -3

Lastly, create your new equation in slope-intercept form with the values you have found.

  • y = -1/3x -3
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