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Sagot :
Given:
The point lies on the line is (1/9, -3).
The parallel line is -8y+4x=4.
Required:
We need to find the equation of the line.
Explanation:
Consider the parallel line.
[tex]-8y+4x=4[/tex]Subtract 4x from both sides.
[tex]-8y+4x-4x=4-4x[/tex][tex]-8y=4-4x[/tex]Divide both sides by (-8).
[tex]-\frac{8y}{-8}=\frac{4}{-8}-\frac{4x}{-8}[/tex][tex]y=-\frac{1}{2}+\frac{1}{2}x[/tex][tex]y=\frac{1}{2}x-\frac{1}{2}[/tex]Which is of the form
[tex]y=mx+b[/tex]where slope,m=1/2.
We know that the slope of the parallel lines is the same.
The slope of the required line is m =1/2.
Consider the line equation.
[tex]y=mx+b[/tex]Substitute x =1/9, y=-3, and m=1/2 in the equation to find the value of b.
[tex]-3=\frac{1}{9}(\frac{1}{2})+b[/tex][tex]-3=\frac{1}{18}+b[/tex]Subtract 1/18 from both sides.
[tex]-3-\frac{1}{18}=\frac{1}{18}+b-\frac{1}{18}[/tex][tex]-3\times\frac{18}{18}-\frac{1}{18}=b[/tex][tex]\frac{-54-1}{18}=b[/tex][tex]b=-\frac{55}{18}[/tex]Substitute m=1/2 and b =-55/18 in the line equation.
[tex]y=\frac{1}{2}x-\frac{55}{18}[/tex]Multiply both sides by 18.
[tex]18y=18\times\frac{1}{2}x-18\times\frac{55}{18}[/tex][tex]18y=19x-55[/tex]Final answer:
[tex]18y=19x-55[/tex]
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