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Leya [2.2K]
2 years ago
13

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 equat

ion of L2.
Mathematics
2 answers:
mariarad [96]2 years ago
7 0
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
Natali [406]2 years ago
3 0

Answer:   x-2y+7=0

Step-by-step explanation:

Given : The  lineL_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

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monitta

Answer:

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