what is the slope and the y intercept of the equation 9+27/2x=-3/2y. write the y-intercept as an ordered pair.
To find the slope and y-intercept of the equation 9 + 27/2x = -3/2y, we need to rewrite the equation into slope-intercept form, which is y = mx + b.
First, let's isolate y on one side of the equation:
9 + 27/2x = -3/2y
-3/2y = 9 + 27/2x
y = (-2/3)(9 + 27/2x)
y = -6 - 27x/2
Now that we have y in terms of x, we can identify the slope and y-intercept.
The slope (m) is the coefficient of x, which is -27/2.
The y-intercept is the value of y when x = 0. Plug in x = 0 into the equation to find y:
y = -6 -27(0)/2
y = -6
Therefore, the y-intercept is (0, -6).