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

Answer:

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

Step-by-step 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:

$3x+2y=-9\\3x-3x+2y=-9-3x\\2y=-3x-9\\y=\frac{-3}{2}x-\frac{-9}{2}$

Therefore, slope is $-\frac{3}{2}$ and y intercept is $-\frac{9}{2}$.

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.