MATH SOLVE

5 months ago

Q:
# the line L1 has equation 2x + y = 8. The line L2 passes through the point A ( 7, 4 ) and is perpendicular to L1 . Find the equation of L2.

Accepted Solution

A:

the formula to find linear eqution of graph is

y=mx+c

m= gradient

c= y intercept

first find what is the gradient of L1. In order to get the gradient make y the subject. thus,

2x+y=8

y=-2x+8

thus, the gradient of L1 is -2.

The question states that L2 is perpendicular to L1, thus the gradient of L2 is reciprocal to gradient of L1.

Thus, gradient of L2 will be

m= 1/2

In order for the gradient to be reciprocal, it needs to be perpendicular.

thus so far the equation of L2 is

y= 1/2x+c

Now the question states that is passes through A(7,4). Thus you need to sub in x=7 and y=4 into equation of L2 to find what is the y intercept.

4= 1/2(4)+c

c=2

thus the equation of L2 is

y=1/2x+2

y=mx+c

m= gradient

c= y intercept

first find what is the gradient of L1. In order to get the gradient make y the subject. thus,

2x+y=8

y=-2x+8

thus, the gradient of L1 is -2.

The question states that L2 is perpendicular to L1, thus the gradient of L2 is reciprocal to gradient of L1.

Thus, gradient of L2 will be

m= 1/2

In order for the gradient to be reciprocal, it needs to be perpendicular.

thus so far the equation of L2 is

y= 1/2x+c

Now the question states that is passes through A(7,4). Thus you need to sub in x=7 and y=4 into equation of L2 to find what is the y intercept.

4= 1/2(4)+c

c=2

thus the equation of L2 is

y=1/2x+2