Question

Which statement explains the lines 2x+y=4 and y=1/2x+4 are related

Answer 1

Answer:

The lines are perpendicular

Step-by-step explanation:

we have

$2x+y=4$

isolate the variable y

$y=-2x+4$ ----> equation A

The slope of the line A is $m=-2$

$y=\frac{1}{2}x+4$ -----> equation B

The slope of the line B is $m=\frac{1}{2}$

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

In this problem

The slopes of line A and line B are opposite reciprocal

therefore

The lines are perpendicular

Answer 2

Answer:

The two lines are perpendicular as the multiplication of the two slopes of corresponding equations is -1.

• $\frac{1}{2}\times-2=-1$

• $m_1 \times m_2 = - 1$

Step-by-step explanation:

As the given equations

$2x+y=4$ and $y=1/2x+4$

We have to determine the relationship between lines.

Let us consider

$2x+y=4$.....[A]

$y=1/2x+4$.....[B]

As we know that slope intercept form of an equation is

$y=mx+c$

Here, m is the slope of the equation.

Compare $y=1/2x+4$ with $y=mx+c$

Let us consider m₁ be the slope of $y=1/2x+4$

$y=1/2x+4$ has a slope $m_{1}=\frac{1}{2}$

Solving Equation [A]

$2x+y=4$

$y=-2x+4$......[C]

Compare $y=-2x+4$ with $y=mx+c$

Let us consider m₂ be the slope of $y=-2x+4$

$y=-2x+4$ has a slope $m_{2}=-2$

Two lines will be perpendicular if the multiplication of the two slopes of corresponding equations is -1.

i.e. $m_1 \times m_2 = - 1$

As

• $y=1/2x+4$ has a slope $m_{1}=\frac{1}{2}$

• $y=-2x+4$ has a slope $m_{2}=-2$

So, lets multiply the slopes of equations [A] and [B].

$\frac{1}{2}\times-2=-1$

$m_1 \times m_2 = - 1$

Therefore, the two lines are perpendicular. Please also check the attached figure to visualize the relationship.

Keywords: lines, perpendicular lines, slope

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