How do I turn this equation into a perpendicular and parallel line in standard form?

Question

I had to turn the equation, y - 3 = 3 (x + 1), into a perpendicular line that passes through (5,-1) and I got y = -1/3x + 2/3. Would the standard form of this be 1x + 3y = 2? I then have to find the x-intercept of this. The parallel line passes through (0,-3) and I got y = 3x + -3 but I do not know the standard form. On the paralell line, I also have to find the ordered pair where x = 2.

Answer 1

To find the x-intercept of x + 3y = 2, plug in 0 for y and solve for x:

 

x + 3y = 2

x + 3(0) = 2

x = 2

 

The x-intercept is (2,0).

 

To convert y = 3x - 3 into standard form, subtract 3x from both sides:

 

y = 3x - 3

-3x + y = -3

 

Then, plug in 2 for x and solve for y to get your point:

 

-3x + y = -3

-3(2) + y = -3

-6 + y = -3

y = 3

 

Your point is (2,3).