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-intercept form of the equation, we need to rewrite it in the form y = mx + b, where m is the slope and b is the y-intercept.
First, let's rewrite the given equation:
9 + (27/2)x = (-3/2)y
Multiplying both sides of the equation by (-2/3), we get:
(-2/3)(9 + (27/2)x) = y
Distributing the (-2/3) to both terms in the parentheses, we have:
(-2/3)(9) + (27/3)x = y
-6 + (9/2)x = y
So, the equation in slope-intercept form is:
y = (9/2)x - 6
Comparing this equation to the slope-intercept form y = mx + b, we can conclude that the slope (m) is 9/2 and the y-intercept (b) is -6.
Writing the y-intercept as an ordered pair, it would be (0, -6).
To find the slope and the y-intercept of the equation 9 + (27/2)x = (-3/2)y, we need to rearrange the equation into the slope-intercept form, which is in the form of y = mx + b, where m represents the slope and b represents the y-intercept.
Let's begin by isolating y on one side of the equation:
9 + (27/2)x = (-3/2)y
To isolate y, we multiply both sides of the equation by -2/3:
(-2/3)(9 + (27/2)x) = (-2/3)(-3/2)y
-6 - 18x/3 = 1y
-6 - 6x = y
Now we have the equation in the form y = mx + b, where the slope m is -6 and the y-intercept b is -6. Therefore, the slope is -6, and the y-intercept is (-6, 0).
To summarize:
Slope (m) = -6
Y-intercept (b) = (-6, 0)
To find the slope and the y-intercept of the equation, we first need to rearrange it into slope-intercept form, which has the form y = mx + b, where m represents the slope and b represents the y-intercept.
Let's start by simplifying the given equation: 9 + 27/2x = -3/2y.
We can rewrite this equation as: -3/2y = 27/2x - 9
Now, let's isolate y by dividing both sides of the equation by -3/2 (or multiplying by -2/3), which gives us: y = -2/3 * (27/2x - 9).
Simplifying further: y = -2/3 * (27/2x) + 2/3 * 9.
y = -9x + 6
By comparing this equation with the slope-intercept form (y = mx + b), we can see that the slope (m) is -9 and the y-intercept (b) is 6.
To write the y-intercept as an ordered pair, we use the form (0, b), where b is the y-intercept. Therefore, the y-intercept can be written as (0, 6).
In summary:
Slope (m) = -9
Y-intercept (b) = 6
Y-intercept as an ordered pair = (0, 6)