What is an equation of the line that passes through the point (6,1) and is perpendicular to the line 2x+3y=18

y = 3/2x -8

Step-by-step explanation:

The first thing you should do is change the equation into slope intercept form. Subtract 2x from both sides to get: 3y = -2x + 18. Divide all parts of the equation by 3 to get your equation in slope intercept: y = -2/3x + 6. One thing you should know when finding the slope of a perpendicular line is that it is the opposite reciprocal. So, the slope is going to be 3/2. This is your current equation: y = 3/2x + b. Plug in the point to the equation, it should look like this: 1 = 3/2(6) + b. Multiply 3/2 by 6 to get 9. This is what it should look like: 1 = 9 + b. Then, subtract 9 from both sides of the equation to get your y-intercept of -8. Go back to your other equation and plug in -8 for b. This is your final equation: y = 3/2x -8. Hope this helped!