If the graph of a line has a positive slope and a negative y-intercept, what happens to the x-intercept if the

Question

If the graph of a line has a positive slope and a negative y-intercept, what happens to the x-intercept if the slope and the y-intercept are doubled?

the x-intercept becomes four times larger

the x-intercept becomes twice as large

the x-intercept becomes one-fourth as large

the x-intercept remains the same

Answer 1

After drawing sample pictures (Deductive Reasoning), I would say the x-intercept becomes one-fourth as large.

Answer 2

The x-intercept remains the same.

y=mx+b

To find the x-intercept, solve for x:

y-b=mx

(y-b)/m=x

(y/m)-(b/m)=x

The x-intercept is -b/m (which is actually a positive number, since we know that b is a negative number and m is a positive number from the problem given)

Now, see what happens when we double both m and b:

y=2mx+2b

y-2b=2mx

(y-2b)/2m=x

(y/2m)-(2b/2m)=x

(y/2m)-(b/m)=x

The x intercept is still -b/m

_/

Answer 3

y = mx + b (m = slope,  b = y-intercept)

The x-intercept is when y = 0

So, is there a difference between these two?

mx + b = 0

2(mx + b ) = 0

The answer is no.  The x-intercept will stay the same.