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 + (27/2)x = - (3/2)y, we need to rewrite it in slope-intercept form, y = mx + b.
To do this, let's first isolate the y term:
(27/2)x = -(3/2)y - 9
Dividing through by -(3/2):
(27/2x) / -(3/2) = (-(3/2)y - 9) / -(3/2)
(-27/6)x = (3/3)y + 9/3
(-9/2)x = (y/1) + 3
Now, let's isolate y:
(y/1) = (-9/2)x - 3
This is in the form y = mx + b, where m is the slope and b is the y-intercept.
From this equation, we can see that the slope (m) is -9/2.
The y-intercept (b) is -3.
So, the y-intercept as an ordered pair is (0, -3).
To find the slope and y-intercept of the equation 9+27/2x = -3/2y, let's begin by rearranging the equation into slope-intercept form, which is in the form of y = mx + b, where m represents the slope, and b represents the y-intercept.
First, we can cross-multiply to eliminate the fractions. Multiply both sides of the equation by 2 to get rid of the denominators:
2 * (9 + 27/2x) = 2 * (-3/2y)
This simplifies to:
18 + 27x = -3y
Now, we can isolate y by dividing both sides of the equation by -3:
(18 + 27x) / -3 = y
Simplifying further, we have:
-6 - 9x = y
Comparing this equation with y = mx + b, we can identify the slope (m) and the y-intercept (b).
The slope (m) is the coefficient of x, which is -9. Therefore, the slope is -9.
The y-intercept (b) is the constant term, which is -6. So, the y-intercept is (-6, 0).