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

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

Answer 2

Answer:   $x-2y+7=0$

Step-by-step 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.

$\Rightarrow\ -2\times p=-1\\\\\Rightarrow\ p=\dfrac{1}{2}$

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 :-

$(y-7)=\dfrac{1}{2}(x-7)\\\\\Rightarrow\ 2y-14=x-7\\\\\Rightarrow\ x-2y+7$