Question

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

Answer 1

no

Answer 2

To find the slope and the y-intercept, we need to rewrite the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

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

First, let's isolate y by multiplying both sides of the equation by -2/3:
-2/3 (9 + 27/2 x) = -2/3 (-3/2 y)
(-2/3)(9) + (-2/3)(27/2) x = (3/2) y
-6 + (-9) x = (3/2) y
-6 - 9x = (3/2) y

Now, divide both sides of the equation by (3/2) to solve for y:
-6 - 9x = (3/2) y
y = (-6 - 9x) / (3/2)
y = -6/(3/2) - 9x/(3/2)
y = -4 - 6x

Comparing this with y = mx + b form, we can see that the slope (m) is -6 and the y-intercept (b) is -4.

Therefore, the slope is -6 and the y-intercept is (-4,0).

Answer 3

Apologies for the incorrect response. Let's find the slope and the y-intercept correctly.

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

First, let's isolate y by multiplying both sides of the equation by -2/3:
(-2/3)(9 + 27/2 x) = (-2/3)(-3/2 y)
-18/3 - (27/2)(2/3) x = (3/2) y
-6 - (9/2) x = (3/2) y

Now, divide both sides of the equation by (3/2) to solve for y:
-6 - (9/2) x = (3/2)y
y = (-6 - (9/2) x) / (3/2)
y = -4 - (3/2)x

Comparing this with y = mx + b form, we can see that the slope (m) is -3/2 and the y-intercept (b) is -4.

Therefore, the slope is -3/2 and the y-intercept is (-4, 0).