The equations of three lines are given below. Line 1: 2y = 5x+3

Line 2: y= 5/2 x+ 8

Line 3: 4x+10y = 6

Neither

Perpendicular

Parallel

Explanation:

Parallel lines have the same slope (y=mx+b, where m is the slope) and different y-intercepts, perpendicular lines have slopes that are opposite (negative/positive) reciprocals (multiplicative inverses) of each other.

Examples:

Parallel slopes: 3 and 3

Perpendicular slopes: 2 and

−

1

2

Neither: 4 and -8

To find out if the first two lines are parallel or perpendicular or neither, first put both equations into slope-intercept (y=mx+b) form.

Problem 1:

2

x

−

5

y

=

8

2

x

=

8

+

5

y

5

y

=

2

x

−

8

y

=

2

5

x

−

8

5

→

The first line has a slope of

2

5

5

x

−

2

y

=

2

5

x

=

2

+

2

y

2

y

=

5

x

−

2

y

=

5

2

x

−

1

→

The second line has a slope of

5

2

, this is not the opposite reciprocal of the first slope or the same as the first slope; these two lines are neither perpendicular or parallel

Problem 2:

y

=

5

6

x

+

8

→

The slope is

5

6

y

=

−

6

5

x

−

4

→

The lines are perpendicular;

−

6

5

is the opposite reciprocal of

5

6

Problem 3:

x

−

2

y

=

12

x

=

2

y

+

12

2

y

=

x

−

12

y

=

1

2

x

−

6

→

The first line has a slope of

1

2

and a y-intercept of -6

3

x

−

6

y

=

10

3

x

=

6

y

+

10

6

y

=

3

x

−

10

y

=

3

6

x

−

10

6

y

=

1

2

x

−

5

3

→

This line has a slope of

1

2

(same as the first one), but a different y-intercept. These two lines are parallel.

Step-by-step explanation:

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