The line which is parallel to the line 2x + 5y =8 is [tex]y= -\frac{2}{5} x+4[/tex] .
The correct option is (B) [tex]y= -\frac{2}{5} x+4[/tex]
What is parallel line in linear equation in two variables?
If the lines are parallel, there is no solution for the pair of linear equations. If there is no solution of the given pair of linear equations, the equations are called inconsistent.
As we know the condition for two parallel line given by the equation
[tex]a_1 x+b_1y+c_1=0\\a_2x+b_2y+c_2= 0[/tex]
is:
[tex]\frac{a_1}{a_2} \; = \; \frac{b_1}{b_2}[/tex] ≠ [tex]\frac{c_1}{c_2}[/tex]
We have the given equation as 2x + 5y =8
the equation which is parallel to 2x + 5y= 8 be
B) [tex]y= -\frac{2}{5} x+4[/tex]
5y = -2x +20
2x+5y=20
So, it satisfies the condition [tex]\frac{a_1}{a_2} \; = \; \frac{b_1}{b_2}[/tex] ≠ [tex]\frac{c_1}{c_2}[/tex]
Rest of the equation aren't satisfying the condition [tex]\frac{a_1}{a_2} \; = \; \frac{b_1}{b_2}[/tex] ≠ [tex]\frac{c_1}{c_2}[/tex].
Hence the line parallel to 2x+ 5y =8 is [tex]y= -\frac{2}{5} x+4[/tex].
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