Question

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

Answers

  1. Answer:
    2x+y=0
    Step-by-step explanation:
    Given:
    \displaystyle \large{2x+y=4}\\\displaystyle \large{y=-2x+4}
    To find:
    • The equation of line that’s parallel and passes through origin point.
    Parallel Definition:
    • Both lines have same slope.
    Slope-Intercept:
    \displaystyle \large{y=mx+b}
    • m = slope
    • b = y-intercept
    Therefore, another line is:
    \displaystyle \large{y=-2x+b}
    Since the line passes through origin point which is (0,0). Substitute x = 0 and y = 0 in the equation:
    \displaystyle \large{0=-2(0)+b}\\\displaystyle \large{b=0}
    Therefore, the equation is:
    \displaystyle \large{y=-2x}
    Convert back to standards form:
    \displaystyle \large{2x+y=0}
    Therefore, another line that is parallel to \displaystyle \large{2x+y=4} is 2x+y=0

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  2. 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

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