PARALLEL AND PERPENDICULAR LINES FROM GRAPH

Example 1 :

Write down equation of the line parallel to line 1 and passes through A.

Solution :

Slope (m) = Rise/Run

= 10/2

m = 5

Drawing a line parallel to the given line using the slope 5.

Equation of line passes through the point A will have the same slope 

y = 5x - 4

To check our equation, we select one of the point from the line that we have drawn. Say (2, 6)

Applying the point (2, 6) on the line :

6 = 5(2) - 4

6 = 10 - 4

6 = 6

Example 2 :

Write down equation of the line parallel to line 1 and passes through A.

Solution :

To find the slope of the line, we the formula rise/run.

Slope (m) = Rise/Run

In graph, Rise = 4 and Run = 1

= 4/1

m = 4

Equation of line passes through the point A will have the same slope 

y = 4x - 5

To check our equation, we select one of the point from the line that we have drawn. Say (2, 3)

Applying the point (2, 3) on the line :

3 = 4(2) - 5

3 = 8 - 5

3 = 3

Example 3 :

Write down equation of the line parallel to line 1 and passes through A.

Solution :

Slope (m) = Rise/Run

In graph, Rise = 2 and Run = 4, it is falling line. So it will have negative slope.

= -4/2

m = -2

Equation of line passes through the point A will have the same slope 

y = -2x + 8

To check our equation, we select one of the point from the line that we have drawn. Say (2, 4)

Applying the point (2, 4) on the line :

4 = -2(2) + 8

4 = -4 + 8

4 = 4

Example 4 :

Write down the equation of the line perpendicular to the line 1 and passing through A.

Solution :

Choosing two points from the line (0, -2) and (2, 0).

Slope (m) = (0 + 2)/(2 - 0)

m = 2/2

m = 1

Slope of the perpendicular line, which passes through the point A is -1.

Equation of the line passes through A (0, 4) is :

y - 4 = -1(x - 0)

y - 4 = -x

y = -x + 4

So, equation of the required line is y = -x + 4.

Example 5 :

Write down the equation of the line perpendicular to the line 1 and passing through A.

Solution :

Choosing two points from the line (1, 0) and (0, 4).

Slope (m) = (4 - 0)/(0 - 1)

m = 4/(-1)

m = -4

Slope of the perpendicular line, which passes through the point A is 1/4.

Equation of the line passes through A (0, 0) is :

y - 0 = (1/4)(x - 0)

y = x/4

So, equation of the required line is y = x/4.

Example 6 :

Write down the equation of the line perpendicular to the line 1 and passing through A.

Solution :

Choosing two points from the line (0, -8) and (1, 2).

Slope (m) = (2 - (-8))/(1 - 0)

m = (2+8)/1

m = 10

Slope of the perpendicular line, which passes through the point A is -1/10.

Equation of the line passes through A (0, 9) is :

y - 9 = (-1/10)(x - 0)

10(y - 9) = -x

10y - 90 =-x

y = (-1/10)x + (90/10)

y = (-1/10)x + 9

So, equation of the required line is y = (-1/10)x + 9.