are the lines parallel, perpendicular, or neither?

Question

I need help in Geometry!!!!!!!!!!!!!!!!!!

1.) y=3x-2
y=1/3x+2

2.) y=2
x=0

3.) y=1/2x+1
-4y=8x+3

4) y=x
8y-x= 8



and how do you write an equation for the perdendicular to line XY that contains pint z??????????

15.) line XY: 3x+2y=-6, Z (3,2)

Answer 1

This is all about slope.

In an equation of the form: y = m*x + b ,
the coeffiecient m is the slope.

Two lines are parallel if they have the same slope, and perpendicular if one is the negative inverse of the other (like 3 and -1/3, or -7 and 1/7).

On problem 1, the slopes are 3 and 1/3. So, neither.

On problem 3, the slopes are 1/2 and -2 (after you reduce the 2nd equation to be y = -2x - 3/4). So, perpendicular.

On problem 4, the slopes are 1 and 1/8 (after you reduce the 2nd equation to be y = 1/8x + 1)

Problem 2 is a special case. One is a vertical line, and the other a horizontal line. So, perpendicular.

Finally, for problem 15, put the line in slope-intercept form (y = m*x + b). You should get y = -3/2x - 3. Since the slope of this line is -3/2, the slope of your new line will be 2/3.
So our equation will be y = 2/3x + b, where b solves the equation for point Z. Since 3 = 2/3 * 3, b=0. Thus your answer is y = 2/3 x, or 2x - 3y = 0, depending on how you need to write it..

Answer 2

Two lines are parallel if their slopes are equal.
Two lines are perpendicular if the slope of each line is the negative reciprocal of the other.

15) use the second sentence above to find the slope of a perpendicular line. Use the slope and given point to find the equation.

Answer 3

12x + 4y = sixteen 4y = sixteen - 12x y = -3x + 4 slope m1 = -3 (y = mx + c) 5y - 22 = -15x y = -3x + 22/5 slope m2 = -3 hence, the two traces are parallel to a minimum of one yet another considering that they have comparable slope

Answer 4

Parallel lines have the same slope
Inverse lines have -run/rise slop
Non would be neither of these