Question

What is the slope and the y -intercept of the equation 9+27/2x=−3/2y . Write the y -intercept as an ordered pair.(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the slope and the y-intercept of the equation 9 + 27/2x = -3/2y, we first need to rewrite the equation in the slope-intercept form y = mx + b.

Given equation: 9 + 27/2x = -3/2y
Rearrange the equation to solve for y:
27/2x = -3/2y - 9
27/2x = -3/2y - 18/2
27/2x = -3/2y - 9
(27/2)x = (-3/2)y - 9
y = (-2/3)(27/2)x - 9
y = -9x - 9

Now that the equation is in slope-intercept form, we can see that the slope is -9 and the y-intercept is -9.

To write the y-intercept as an ordered pair, we have:
y-intercept = (0, -9)

Answer 2

the y intercept is wrong

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake. Let's find the correct y-intercept.

Given equation: 9 + 27/2x = -3/2y

Rearrange the equation to solve for y:
27/2x = -3/2y - 9
27/2x = -3/2y - 18/2
27/2x = -3/2y - 9
(27/2)x = (-3/2)y - 9
y = (-2/3)(27/2)x - 9
y = -9x - 9

Now, we can see that the slope is -9 and the y-intercept occurs when x = 0.

To find the y-intercept, substitute x = 0 into the equation:
y = -9(0) - 9
y = 0 - 9
y = -9

Therefore, the correct y-intercept is -9.

Writing the y-intercept as an ordered pair, it is (0, -9).