# PARALLEL LINES IN THE COORDINATE PLANE WORKSHEET

## About "Parallel lines in the coordinate plane worksheet "

Parallel lines in the coordinate plane worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on parallel lines in the coordinate plane.

## Parallel lines in the coordinate plane worksheet - Problems

Problem 1 :

In the diagram given below, find the slope of each line. Determine whether the lines jand jare parallel.

Problem 2 :

In the diagram given below, find the slope of each line. Which lines are parallel ?

Problem 3 :

Write an equation of the line through the point (2, 3) that has a slope 5.

Problem 4 :

In the diagram given below,

Line n1 has the equation y  =  -x/3 -1.

Line n2 is parallel to the line n1 and passes through the point (3, 2).

Write the equation of the line n2.

## Parallel lines in the coordinate plane worksheet - Solution

Problem 1 :

In the diagram given below, find the slope of each line. Determine whether the lines j1 and j2 are parallel.

Solution :

Line j1 has a slope of

m2  =  4/2  =  2

Line j2 has a slope of

m2  =  2/1  =  2

Since the slope of the lines jand jare equal, the lines jand jare parallel.

Problem 2 :

In the diagram given below, find the slope of each line. Which lines are parallel ?

Solution :

Part 1 :

Find the slope of the line k1. Line k1 is passing through the points (0, 6) and (2, 0).

Let (x1, y1) =  (0, 6) and (x2, y2)  =  (2, 0)

Slope (k1)  =  (y2 - y1)  / (x2 - x1)

Slope (k1)  =  (0 - 6)  / (2 - 0)

Slope (k1)  =  - 6 / 2

Slope (k1)  =  - 3

Part 2 :

Find the slope of the line k2. Line k2 is passing through the points (-2, 6) and (0, 1).

Let (x1, y1)  =  (-2, 6) and (x2, y2)  =  (0, 1)

Slope (k2)  =  (y2 - y1)  / (x2 - x1)

Slope (k2)  =  (1 - 6)  / [0 -(-2)]

Slope (k2)  =  (1 - 6)  / [0 + 2]

Slope (k2)  =  - 5/2

Part 3 :

Find the slope of the line k3. Line k3 is passing through the points (-6, 5) and (-4, 0).

Let (x1, y1)  =  (-6, 5) and (x2, y2)  =  (-4, 0)

Slope (k3)  =  (y2 - y1)  / (x2 - x1)

Slope (k3)  =  (0 - 5)  / [-4 - (-6)]

Slope (k3)  =  - 5 / (-4 + 6)

Slope (k3)  =  - 5 / 2

Compare the slopes. Because k2 and k3 have the same slope, they are parallel. Line k1 has a different slope, so it is not parallel to either of the lines.

Problem 3 :

Write an equation of the line through the point (2, 3) that has a slope 5

Solution :

Slope-intercept form equation of a line :

y  =  mx + b ------(1)

Substitute (x, y)  =  (2, 3) amd m  =  5

3  =  5(2) + b

Simplify

3  =  10 + b

Subtract 3 from both sides

-7  =  b

The equation of the required line is

(1) ------> y  =  5x - 7

Problem 4 :

In the diagram given below,

Line n1 has the equation y  =  -x/3 -1.

Line n2 is parallel to the line n1 and passes through the point (3, 2).

Write the equation of the line n2.

Solution :

The slope of the line n1 is -1/3. Because the lines n1 and n2 are parallel, they have the same slope. So, the slope of the line n2 is also -1/3.

Slope-intercept form equation of a line :

y  =  mx + b ------(1)

Because the line n2 is passing through (3, 2), substitute aa(x, y)  =  (3, 2) amd m  =  -1/3

2  =  (-1/3)(3) + b

Simplify

2  =  -1 + b

3  =  b

The equation of the required line is

(1) ------> y  =  (-1/3)x + 3

y  =  -x/3 + 3

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