ahmer2208
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Find the equation of a line which is parallel to the line with the equation 2x + y = 4 and
which passes through the origin.

Respuesta :

Answer:

y = -2x

Step-by-step explanation:

Given

  • 2x + y = 4
  • Passes through the origin (0, 0)

Solving

Rewriting the equation

  • 2x + y = 4
  • y = -2x + 4

New equation

  • The slope of the new line is the same (-2) because it is parallel
  • The y-intercept is (0, 0)

⇒ y = mx + b [m = slope, b = y-intercept]

⇒ y = -2x + 0

⇒ y = -2x

VectorFundament120

Answer:

2x+y=0

Step-by-step explanation:

Given:

[tex]\displaystyle \large{2x+y=4}\\\displaystyle \large{y=-2x+4}[/tex]

To find:

  • The equation of line that’s parallel and passes through origin point.

Parallel Definition:

  • Both lines have same slope.

Slope-Intercept:

[tex]\displaystyle \large{y=mx+b}[/tex]

  • m = slope
  • b = y-intercept

Therefore, another line is:

[tex]\displaystyle \large{y=-2x+b}[/tex]

Since the line passes through origin point which is (0,0). Substitute x = 0 and y = 0 in the equation:

[tex]\displaystyle \large{0=-2(0)+b}\\\displaystyle \large{b=0}[/tex]

Therefore, the equation is:

[tex]\displaystyle \large{y=-2x}[/tex]

Convert back to standards form:

[tex]\displaystyle \large{2x+y=0}[/tex]

Therefore, another line that is parallel to [tex]\displaystyle \large{2x+y=4}[/tex] is 2x+y=0

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