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UNO [17]
3 years ago
7

Slope of line a is ½. What is the equation of a line that is parallel to line a? Y+½x=2 -2x+y+2=0 2x-2=y -½x+y-2=0

Mathematics
1 answer:
sasho [114]3 years ago
6 0

Answer:

The equation of a line that is parallel to line a is y=½x + 2, or what is the same -½x+y-2=0

Step-by-step explanation:

A line is a polynomial function of the first degree that has the following form:

y = m * x + b

where m is the slope of the line and b is the intercept with the Y axis.  The slope is the inclination of the line with respect to the abscissa axis.

In this case you know that the slope of line a is ½.  

Parallel lines are two or more lines in a plane that never intersect. Two lines are parallel if they have the same slope and different y-intercepts.

You have:

  • y+½x=2       →       y= -½x +2
  • -2x+y+2=0       →       y=2x -2
  • 2x-2=y      
  • -½x+y-2=0       →       y=½x + 2

The line that has the same slope as line a is the last one, so <u><em>the equation of a line that is parallel to line a is y=½x + 2, or what is the same -½x+y-2=0</em></u>

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svetlana [45]

Answer:  The required solution is

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Step-by-step explanation:   We are given to solve the following differential equation :

y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(i)

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y(t)=(A+Bt)e^{-5t}.

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y(0)=-2\\\\\Rightarrow A=-2

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y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.

Thus, the required solution is

y(t)=(-2+1\times t)e^{-5t}\\\\\Rightarrow y(t)=(-2+t)e^{-5t}.

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