Question

Select the line that will never intersect with the line that has the equation $y=4x+2$.

• A. $y+4x=3$
• B. $2y+4x=3$
• C. $y-4x=-3$
• D. $y+4x=-2$
• E. $y+\frac{1}{4}=3$

Answer 1

Answer: (C)

$y-4x=-3$

The given equation of line is $y=4x+2$

The slope of the line $m=4$

$\Rightarrow$ Slope of line $y+4x=3$ is $-4$

$\Rightarrow$ Slope of line $2y+4x=3$ is $-4$

$\Rightarrow$ Slope of line $y-4x=-3$ is $4$

$\Rightarrow$ Slope of line $y+4x=-2$ is $-4$

$\Rightarrow$ Slope of line $y+\frac{1}{4}=3$ is $0$

So we can see every line written above will intersect the given line except $y-4x=-3$, which has slope same as Given line. i.e. $m=4$

Hence the line in the equation $y-4x=-3$ is parallel to given line, hence it will never intersect the given line.

Correct option is $C$.