Write an equation for a line that is perpendicular to the line 8x-4y=12 and passes throught the origin
1 answer:
Answer:
y= -x
Step-by-step explanation:
First, let's put the line in y=mx+b form
8x-4y=12
Subtract 8x over
-4y= -8x+12
Then divide everything by -4
y=2x-3
To find the perpendicular slope, negate the slope and flip the numerator and the denominator
Original Slope: 2/1
Flip: 1/2
Negate: -1/2
Then, use the point slop formula to find the equation of the line.
(y-)=m(x-
)
Insert (0,0) in for and -1/2 in for m
y-0= -1/2(x-0)
Distribute the -1/2
y-0= -1/2x+0
Add the 0 over
y= -1/2x
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So we have the system of equations:
equation (1)
equation (2)
To use substitution, we are going to solve for one variable in one of our equations, and then we are going to replace that value in the other equation:
Solving for
in equation (2):
equation (3)
Replacing equation (3) in equation (1):
equation (4)
Replacing equation (4) in equation (3):
We can conclude that the solution of our system of equations is <span>(7/5, 21/10)</span>
To use substitution, we are going to solve for one variable in one of our equations, and then we are going to replace that value in the other equation:
Solving for
Replacing equation (3) in equation (1):
Replacing equation (4) in equation (3):
We can conclude that the solution of our system of equations is <span>(7/5, 21/10)</span>