perpendicular or parallel lines

Question

1) Which describes the lines represented by these equations?  

 

y=1/6x+6

y=2/12x+6

 

a. conincident lines

b. intersecting lines

c. parallel lines

d. vertical lines

 

2)  Which best describes the graphs of the line that has a slope of -2/5 and passes through (10, -2) and the line that passes through (0,1) and (5, -1)?

a. conincident lines

b. intersecting lines
c. parallel lines
d. vertical lines

 

Answer 1

Hi again Andrea;

(1)

y=1/6x+6
y=2/12x+6

 

This lines are coincident lines.  These have the same slope; (1/6) and (2/12) which is also (1/6).  These also have the same y-intercept of 6.  Both lines pass the y-axis at the same point of (0,6).

 

2)

The first line is...

y-y₁=m(x₁-x)

y--2=(-2/5)(y-10)

y+2=(-2/5)(y-10)

y+2=(-2/5)y+4

y=(-2/5)y+2

This has a slope of -2/5, and a y-intercept of 2.

 

The slope of the second line is...

m=(y-y₁)/(x-x₁)

m=(1--1)/(0-5)

m=2/-5

m=-2/5

The slope is -2/5 and the y-intercept, value of y when x=0, is provided as 1.

y=mx+b

y=(-2/5)+1

 

The slope of the two lines, -2/5, is identical and their y-intercepts of 2 and 1 are different.  Henceforth, these are parallel.

Answer 2

1) a, since they are the same line.

2) c, since they have the same slope of -2/5, but do not share the same line.