Mathematics

Question

Line CD passes through (0, 1) and is parallel to x + y = 3. Write the standard form of the equation of line CD.
a. x + y = 1
b. x – y = 1
c. x + 1 = y
d. x + y = 11

2 Answer

  • A. would be the correct choice because the x+y hast to =1.
  • Answer: a. [tex]x+y=1[/tex]

    Step-by-step explanation:

    Given: Line CD passes through (0, 1) and is parallel to [tex]x+y=3[/tex].

    We know that if two line are parallel then they have equal slopes.

    Thus, the slope of line = slope of line [tex]x+y=3[/tex].

    [tex]x+y=3\\\Rightarrowy=3-x[/tex] when we compare this to the standard linear equation  [tex]y=mx+c[/tex].we get  [tex]m=-1[/tex].

    Hence, slope of CD (m)= -1

    Now, the equation of line CD passing through (0,1) is given by :-

    [tex](y-1)=m(x-0)\\\Rightarrow(y-1)=(-1)x\\\Rightarrow x+y=1[/tex]

    Thus, the equation of line CD = [tex]x+y=1[/tex]

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