Question

Which of the following equations represents a line with a negative slope and a negative y-intercept?

Select one:
A. 3x+2y=−9
B. x−y=−3
C. y=4x−6
D. y=−5x+8

Answer 1

A.
`3x+2y=-9`

Explanation:

The standard form of a line in slope-intercept form is:

`y=mx+b`

Where,
`m` is the slope and
`b` is the y-intercept.

Now, let us convert each option in this form.

Option A:

`3x+2y=-9\\3x-3x+2y=-9-3x\\2y=-3x-9\\y=(-3)/(2)x-(-9)/(2)`

Therefore, slope is
`-(3)/(2)` and y intercept is
`-(9)/(2)`.

Both slope and y intercept are negative. So, option A is correct.

Option B:

`x-y=-3\\x-x-y=-3-x\\-y=-x-3\\y=x+3`

Slope is 1 and y intercept is 3. Both are positive. So, option B is incorrect.

Option C:

`y=4x-6`

Slope is 4 and y intercept is -6. Both are not negative. So, option C is incorrect.

Option D:

`y=-5x+8`

Slope is -5 and y intercept is 8. Both are not negative. So, option D is incorrect.