Answer: y = -1/3x - 3
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.