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The line [tex]L_1[/tex] has the equation [tex]2x + y = 8[/tex]. The line [tex]L_2[/tex] passes through the point [tex]A (7, 4)[/tex] and is perpendicular to [tex]L_1[/tex]. Find the equation of [tex]L_2[/tex].

Answer :

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

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