Does the line with equation ax + by = c, where a, b and c are real con

Hi,
ONLY line that will not cross x axis is the line parallel to x axis...
THe equation of line parallel to x axis is y=b..
so if ax+by = c has to be parallel to x- axis, a should be 0..

lets see the statements..

(1) b not equal to 0
This tells us that the line is not parallel to y-axis
Insuff

(2) ab>0
this tells us that neither of a or b is 0..
so the line crosses the x-axis
Suff

B
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Another way:

If line ax+by=c does cross x axis then, there will be a point (z,0) on this line. Which means:

az=c. or z= (c/a). z should have real value and this will be possible when a is not equal to zero.

So our question now becomes: Is a = 0?

statement 1: b not equal to 0; This does not tell anything about a. NS

statement 2: ab>0. a is certainly not equal to 0. Sufficient.


B is the answer.

(Note that if we put z = (c/a) in equation; and we know that a is not equal to zero; we get: (b)(y)=0; Now because statement (2) also says b is not equal to zero, so y will have to be zero. This is what we want and this proves the point that this line cuts x axis. )

Hi chetan2u,

I have one doubt. If a line passes through origin, then can we say that the line passes through x and y axis both...?
Please assist.
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Yes, Prakhar the line passing through ORIGIN crosses x-axis at x=0 and y-axis at y=0...
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We are given a line with equation ax+by = c, where a,b and c are real constants, and we need to determine whether it crosses the x-axis. Let’s start by isolating y in our given equation:

ax+by = c

by = -ax + c

y = (-a/b)x + (c/b)

We now have the given equation in slope-intercept form; the slope is -a/b and the y-intercept is c/b.

Statement One Alone:

b not equal to 0

Since we are not provided any information about the slope of the line, statement one is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

ab>0

Since ab > 0, neither a nor b can be 0. This means that the slope of the line is not equal to zero. Recall that if the slope of a line is 0, the line is horizontal and will not cross the x-axis unless the line is the x-axis itself. Thus, regardless of the values of a or b, the line will, at some point, cross the x-axis.

Answer: B
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A line will always cross x-axis if the slope of line is NOT zero

ax + by = c can be written as \(y = (-\frac{a}{b})x + (\frac{c}{b})\)

Comparing it with \(y = mx+c\) where m is the slope

i.e. SLope of the given line \(= -\frac{a}{b}\)

Question REPHRASED: Is \(-\frac{a}{b}=0\)

Statement 1: b ≠ 0

but a may be 0 or non-zero hence

NOT SUFFICIENT

STatement 2: ab > 0

i.e. ab≠0

i.e. slope is non-zero i.e it will always cross x axis hence

SUFFICIENT

Answer: option B
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Equation: ax+by=c
Rearranging, we get

y = (-a/b)x + (c/b)

Q: Does the line cross the x-axis? We need to find if the slope is 0 or not.

Statements:

(1) b ≠ 0

Doesn't tell anything about a. a can be 0 (line won't cross) or a can be something else (line will cross).

Insufficient.

(2) ab>0

Either a and b are both positive or both negative. Neither a nor b is equal to 0.

Therefore, we know that a is never zero. Does the line cross the x-axis? Definitely Yes.

Sufficient

Hence, the answer is Option (B).[/b]

Eqn of line y =-ax/b+c/b
#1
B not = 0
Insufficient
#2
Ab>0

Possible when both are - or +

So eqn of line y=-x+c and y =-x-c

For values of x & y line will pass x axis slope is not 0
sufficient option B

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