What is the X intercept of non horizontal line

Question

What is the X intercept of non horizontal line m?

(1) The slope of m is 4 times the y intercept of m
(2) The y intercept of line m is -2.

I would like to see the graphical approach for Statement 1. I'm able to find the answer using algebraic approach, however graphical approach is giving me an incorrect answer.

Your help will be appreciated.

Thanks
imhimanshu

Zarrolou · Answer

What is the X intercept of non horizontal line m? 
 y=mx+q

1) The slope of m is 4 times the y intercept of m 
 m=4q 
 y=4qx+q ,or  y=q(4x+1)  the X intercept of that line is  -\frac{1}{4}  as y=q(4x+1)=0 (because q cannot be zero) gives us 4x+1=0.

2) The y intercept of line m is -2. 
 y=mx-2 .
Not sufficient

Take a look at the image, there are three lines y=4x+1, y=8x+2 and y=-4x-1.
Hope it clarifies

kpali · Answer

Algebraic Approach:

We know that the line is not horizontal, Hence is has a a X and a Y intercept.
Case 1) Considering the line in the form: Y=PX+C, P being the slope and C being the constant which is also the Y Intercept.
slope of m is 4 times the y intercept of m, Hence,
P=4C
Y=4CX+C
To find the X intercept, Substituting Y=0
X=-1/4
Sufficient.
Case 2)Y Intercept of line = -2
Hence, in the line Y=PX+C, C = -2
Substituting
Y=PX-2
To find the X intercept, substituting Y=0
X=2/P
P is still u known.
Hence, Insufficient.

Since, Case 1 is sufficient, A is the answer.

prasun9 · Answer

A graphical approach would be to assume the line passes through (0, y) and (x, 0). Where x & y are not equal to zero. Which means x & y are the X and Y intercepts respectively.
 Slope = \frac{(y - 0)}{(0 - x)} = 4y  =>  \frac{-y}{x} = 4y

Since x and y are not equal to 0, multiply each side by  \frac{x}{4y} 
 x = \frac{-1}{4}

Notice we haven't assumed the sign of the intercepts and still we got just one value for the X intercept. Hence Stmt 1 is sufficient.

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What is the X intercept of non horizontal line

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