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

Answer 1

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

First, let's simplify the equation:
9 + (27/2)x = (-3/2)y.

To make it easier to manipulate, let's multiply every term by -2/3 to isolate y:
(-2/3)(9 + (27/2)x) = y.

Distributing the -2/3 on the left side, we have:
-6 - 18x/3 = y,
-6 - 6x = y.

The equation is now in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Thus, the slope, m, is -6 and the y-intercept, b, is -6.

The y-intercept can be written as an ordered pair as (0, -6).