What is the slope and y-intercept of the equation 9 + 27/2x = -3/2y Write the y-intercept as an ordered pair. (1 point)
To find the slope-intercept form of the equation, first isolate the y variable:
9 + 27/2x = -3/2y
27/2x = -3/2y - 9
27/2x = -3/2y - 18/2
27/2x = -3/2y - 18/2
27/2x = -3/2y - 9
27/2x = -3/2y - 9
27x = -4y - 18
Divide by -4 to isolate y:
-27/4x = y + 9
-27/4x - 9 = y
y = -27/4x - 9
The slope is -27/4 and the y-intercept is -9. So, the y-intercept as an ordered pair is (0,-9).
how do we go from 27/2x = -3/2y -9 to 27x = -4y - 18
Apologies for the mistake in my previous response. Let's correct the calculation:
Starting from 27/2x = -3/2y - 9, we want to get rid of the denominators by multiplying by 2 to get rid of the fractions:
2 * 27/2x = 2*(-3/2)y - 2*9
54x = -3y -18
Rearranging the equation in terms of y to get the slope-intercept form (y = mx + b):
3y = -54x - 18
y = -54/3x - 18/3
y = -18x - 6
Therefore, the slope of the equation is -18 and the y-intercept is -6. The y-intercept as an ordered pair is (0, -6). Thank you for pointing out the error, and I appreciate your attention to detail.
neither the slope or y-intercept with BOTH of your answers were correct
I apologize for the mistakes in my previous responses. Let's correct it:
Given the equation 9 + 27/2x = -3/2y, we want to rewrite it in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
First, isolate the y variable:
27/2x = -3/2y - 9
27x = -3y - 18
Dividing by -3 to get y by itself:
-9x = y + 6
y = -9x - 6
Now, the slope is -9 and the y-intercept is -6.
Therefore, the slope of the equation is -9 and the y-intercept is -6. The y-intercept as an ordered pair is (0, -6). Thank you for your patience, and I apologize for the errors in my previous responses.
okay now you're on the right track, the slope is correct, now what is the y-intercept with the information you've unlocked
Given that the equation is in the form y = -9x - 6, the y-intercept is the value of y when x = 0.
y = -9(0) - 6
y = 0 - 6
y = -6
So, the y-intercept is -6.
Therefore, the slope of the equation is -9 and the y-intercept is -6. The y-intercept as an ordered pair is (0, -6). Thank you for guiding me through the solution.
the y-intercept is still incorrect
I apologize for the error. Let's correct it:
Given the equation y = -9x - 6, we know that the y-intercept occurs when x = 0.
Substitute x = 0 into the equation:
y = -9(0) - 6
y = -6
Therefore, the y-intercept is -6, and we can express it as the ordered pair: (0, -6).
Thank you for your patience, and I appreciate your guidance.