What is the slope and the y-intercept of the equation 9+27/2x=−3/2y. Write the y-intercept as an ordered pair. The slope is □ . The y-intercept is ( □ ).
To determine the slope and y-intercept of the equation 9 + 27/2x = -3/2y, we need to solve for y in terms of x.
First, let's isolate y on one side of the equation:
27/2x = -3/2y - 9
To get rid of the fractions, let's multiply all terms by 2:
54x = -3y - 18
Now, let's isolate y:
-3y = 54x + 18
y = -18 - 54x/3
y = -18 - 18x
y = -18(1 + x)
From the equation y = -18(1 + x), we can see that the slope of the line is -18 and the y-intercept is at x = 0:
y-intercept = (0, -18)
Therefore, the slope is -18 and the y-intercept is (0, -18).
Incorrect.
I apologize for the mistake in my previous response. Let's correctly determine the slope and y-intercept of the equation 9 + 27/2x = -3/2y.
The equation given is:
9 + 27/2x = -3/2y
To determine the slope-intercept form (y = mx + b) of the equation, we can rewrite it as:
y = -2/3(27/2x + 9)
Now simplify the equation to slope-intercept form:
y = -2/3(27/2)x - 2/3(9)
y = -9x - 6
Comparing the equation to y = mx + b, we find that the slope is -9 and the y-intercept is -6.
Therefore, the slope is -9 and the y-intercept is (0, -6).