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 y-intercept are doubled?

A) The x-intercept becomes 4 times larger
B) The x-intercept becomes twice as large
C) The x-intercept becomes 1/4th as large
D) The x-intercept remains the same

I need the answer, but also how I would figure this out myself. Thanks!

Well, isn't this an interesting question! Let's break it down, shall we?

If the graph of a line has a positive slope and a negative y-intercept, we know that the line is slanting upwards from left to right and crosses the y-axis below the origin.

Now, let's consider what happens if we double both the slope and y-intercept. Doubling the slope means that the line will become steeper, while doubling the y-intercept means that the point at which the line crosses the y-axis will move further downwards.

If you think about it, doubling the slope doesn't affect where the line crosses the x-axis, also known as the x-intercept. The x-intercept is determined by where the line intersects with the x-axis, which is independent of the slope.

On the other hand, doubling the y-intercept will change the position of where the line crosses the x-axis. Since the y-intercept is negative, doubling it will move the x-intercept towards the origin, making it closer to the y-axis.

So, to answer your question, if we double both the slope and y-intercept, the x-intercept becomes 1/4th as large. This means that option C) is the correct answer.

I hope that helps! And remember, math can be as fun as juggling flaming bowling pins if you look at it the right way. Well, maybe not that fun, but close enough!

To determine what happens to the x-intercept when the slope and y-intercept are doubled, we can analyze the relationship between these variables.

Let's assume the original equation of the line is y = mx + b, where m represents the slope and b represents the y-intercept.

Given that the slope is positive and the y-intercept is negative, we can rewrite the equation as y = mx - |b|.

Now, if we double the slope and the y-intercept, the new equation becomes y = 2mx - 2|b|.

To find the x-intercept, we set y = 0:

0 = 2mx - 2|b|

Dividing both sides of the equation by 2m:

x = -|b| / m

From this equation, we can see that when we double the slope and the y-intercept, the x-intercept will still be determined by the ratio -|b| / m.

So, the correct answer is D) The x-intercept remains the same.

To determine what happens to the x-intercept when the slope and y-intercept are doubled, we need to understand the relationship between the slope-intercept form of a linear equation and the x-intercept.

The slope-intercept form of a linear equation is given by: y = mx + b, where m represents the slope and b represents the y-intercept. The x-intercept occurs when y = 0, so we can substitute this value into the equation to solve for x-intercept.

Given that the slope (m) is positive and the y-intercept (b) is negative, we can conclude that the line is slanting upwards from left to right and crosses the y-axis below the origin.

Now, to determine what happens to the x-intercept when the slope and y-intercept are doubled, we can double the values of m and b in the equation.

Let's call the new slope and y-intercept as 2m and 2b, respectively.

The equation of the new line would be: y = 2mx + 2b

To find the x-intercept of the new line, we substitute y = 0 into the equation:
0 = 2mx + 2b
-2b = 2mx
x = -b/m

Comparing this with the original x-intercept, which was x = -b/m, we can see that both x-intercepts are the same.

Therefore, the answer is:

D) The x-intercept remains the same.

B....

No A
Or it could be C
But D looks right