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sammy [17]
3 years ago
10

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

Mathematics
2 answers:
Inessa [10]3 years ago
4 0

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

Stella [2.4K]3 years ago
4 0

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.

<em>Keywords: lines, perpendicular lines, slope</em>

<em> Learn more about the relationship of lines from brainly.com/question/11186985</em>

<em> #learnwithBrainly</em>

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