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Bunuel
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ax + by + c = 0 is termed as a first-degree equation in x and y. When 08 Oct 2021, 08:45
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E
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45% (medium)

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67% (01:58) correct 33% (01:40) wrong based on 109 sessions

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ax + by + c = 0 is termed as a first-degree equation in x and y. When the solution of the given equation, ax + by + c =0 is plotted on a graph it yields a straight line L. Now, which of the following must be true?

I. If a = 0 and b ≠ 0, then L will be a horizontal line.
II. If b = 0 and a ≠ 0, then L will be a vertical line.
III. If c = 0, then L passes through the origin.

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II and III
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E
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ax + by + c = 0 is termed as a first-degree equation in x and y. When 17 Oct 2021, 03:51
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Bunuel
ax + by + c = 0 is termed as a first-degree equation in x and y. When the solution of the given equation, ax + by + c =0 is plotted on a graph it yields a straight line L. Now, which of the following must be true?

I. If a = 0 and b ≠ 0, then L will be a horizontal line.
II. If b = 0 and a ≠ 0, then L will be a vertical line.
III. If c = 0, then L passes through the origin.

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II and III
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Change it to the common eqn. of a line

\(by = -ax-c \)

\(y= \frac{-a}{b}x - \frac{c}{b}\)


I. If \(a = 0\) and \(b ≠ 0,\) then L will be a horizontal line-> From the simplified eqn we can see, if \(a \) is zero then slope will be zero,and any line with a zero slope is a horizontal line. Hence this will be a horizontal line.True

II. If \(b = 0\) and \(a ≠ 0,\) then L will be a vertical line-> According to the eqn. if \(b=0\) then the eqn. becomes undefined or in other words slope becomes infinite( undefined ), infinite slope means that the line is vertical. Hence True.

III. If \(c = 0,\) then L passes through the origin-> If \(c=0\) means \(y-\) intercept is zero ,which means that the given line meets the \(y \) axis at \(y=0 \), the point \(y=0\) is the orgin. Hence True.

Ans -E

Hope it's clear.
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ax + by + c = 0 is termed as a first-degree equation in x and y. When 31 Mar 2023, 04:18
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Bunuel
ax + by + c = 0 is termed as a first-degree equation in x and y. When the solution of the given equation, ax + by + c =0 is plotted on a graph it yields a straight line L. Now, which of the following must be true?
I. If a = 0 and b ≠ 0, then L will be a horizontal line.
II. If b = 0 and a ≠ 0, then L will be a vertical line.
III. If c = 0, then L passes through the origin.

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II and III
Show more
Solution:

  • We are given equation of a straight line \(ax+by+c=0\)

    I. If \(a = 0\) and \(b ≠ 0\)
    • \(ax+by+c=0\)
      \(⇒by+c=0\)
      \(⇒y=\frac{-c}{b}\)
    • Line of equation \(y=\frac{-c}{b}\) will be a horizontal line parallel to x-axis passing through (0, -c/b)

    II. If \(b = 0\) and \(a ≠ 0\)
    • \(ax+by+c=0\)
      \(⇒ax+c=0\)
      \(⇒x=\frac{-c}{a}\)
    • Line of equation \(x=\frac{-c}{a}\) will be a vertical line parallel to y-axis passing through (-c/a, 0)

    III. If \(c = 0\)
    • \(ax+by+c=0\)
      \(⇒ax+by=0\)
      \(⇒ax=-by\)
    • Line of equation \(ax=-by\) will pass through origin because it satisfies the coordinate (0, 0)

Hence the right answer is Option E
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