Question

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.

Answer 1

Answer:
`x-2y+7=0`

Explanation:

Given : The line
`L_1` has equation
`2x + y = 8`

In intercept form :
`y =-2x+8`

The slope of
`L_1` =-2 [in intercept form equation of line
`y =mx+c`, m is slope ]

Let p be slope of
`L_2`

We know that when two lines are perpendicular then the product of their slopes is -1.

`\Rightarrow\ -2* p=-1\\\\\Rightarrow\ p=(1)/(2)`

The equation of line having slope 'm' and passing through (a,b) is given by :-

`(y-b)=m(x-a)`

Then , equation of line
`L_2` will be :-

`(y-7)=(1)/(2)(x-7)\\\\\Rightarrow\ 2y-14=x-7\\\\\Rightarrow\ x-2y+7`

Answer 2

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