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:

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.