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

Answer 1

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

Starting with 9 + (27/2)x = (-3/2)y, we can isolate y by multiplying both sides by -2/3:

(-2/3)(9 + (27/2)x) = (-2/3)(-3/2)y
-6 - 18x = 3y

Now divide both sides by 3 to obtain y by itself:

(-6 - 18x)/3 = (3y)/3
-2 - 6x = y

The equation is now in the form y = mx + b, where m is the slope and b is the y-intercept. Comparing the equation to the slope-intercept form, we can see that the slope, m, is -6, and the y-intercept, b, is -2.

Therefore, the slope of the equation is -6, and the y-intercept can be expressed as the ordered pair (0, -2).

Answer 2

Wrong

Answer 3

I apologize for the mistake. Let's correct it.

Starting with 9 + (27/2)x = (-3/2)y, let's isolate y by moving all the terms involving y to the left side and all the terms without y to the right side:

(27/2)x + (3/2)y = -9

Next, multiply the entire equation by 2 to eliminate the fractions:

2 * [(27/2)x + (3/2)y] = 2 * (-9)
27x + 3y = -18

Now, let's rewrite the equation in slope-intercept form y = mx + b:

3y = -27x - 18
y = (-27/3)x - 18/3
y = -9x - 6

Comparing this equation to the slope-intercept form, we can see that the slope, m, is -9, and the y-intercept, b, is -6.

Therefore, the slope of the equation is -9, and the y-intercept can be expressed as the ordered pair (0, -6).