Question

Which of the following equations represents a line that is perpendicular toy = -2x+4 and passes through the point, (4,2)?O A. y= -1/2x+2O B. y= 1/2x+4O C. y= -2xO D. y= 1/2x

Answer 1

Given that

The equation is y = -2x + 4 and we have to find the line perpendicular to the given line and pass through the point (4, 2).

Explanation -

Since the two lines are parallel when the product of their slopes is -1.

$\begin{gathered} Let\text{ the slope of given line is m}_1\text{ and slope of line to be found is m}_2. \\ Then,\text{ } \\ m_1\times m_2=-1 \end{gathered}$

On comparing the given line with the general equation,

y = mx + c

we have m = slope = -2

$\begin{gathered} So\text{ we have} \\ m_1=-2 \\ Then \\ -2\times m_2=-1 \\ m_2=\frac{1}{2} \end{gathered}$

Now we have to find the line with a slope 1/2 and pass through the point (4, 2).

$\begin{gathered} y-2=m_2(x-4) \\ y-2=\frac{1}{2}(x-4) \\ y-2=\frac{x}{2}-\frac{4}{2} \\ y-2=\frac{x}{2}-2 \\ y=\frac{x}{2}=\frac{1}{2}x \end{gathered}$

So the required line is y = x/2 and the correct option is D.

Final answer -

Hence the final answer is y = x/2