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What is the slope and the y

-intercept of the equation 9+27/2x=−3/2y
. Write the y
-intercept as an ordered pair.(1 point)
The slope is
. The y
-intercept is (
).

4 answers

To find the slope and the y-intercept from the equation \( 9 + \frac{27}{2}x = -\frac{3}{2}y \), we need to rearrange it into the slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

First, let's isolate \( y \).

Starting with the given equation:

\[ 9 + \frac{27}{2}x = -\frac{3}{2}y \]

We can rearrange this equation by moving all the terms involving \( y \) to one side:

\[ -\frac{3}{2}y = 9 + \frac{27}{2}x \]

Next, multiply both sides by -2 to eliminate the fractions:

\[ 3y = -18 - 27x \]

Now, divide each term by 3:

\[ y = -9 - 9x \]

Now we can identify the slope and y-intercept from this equation:

  • The slope (\( m \)) is -9.
  • The y-intercept (\( b \)) is -9.

The y-intercept as an ordered pair is \( (0, -9) \).

So:

  • The slope is \(-9\).
  • The y-intercept is \( (0, -9) \).
what is the y intercept

To find the y-intercept of the given equation \( 9 + \frac{27}{2}x = -\frac{3}{2}y \), we rearranged it into the slope-intercept form \( y = mx + b \) and derived the following:

\[ y = -9 - 9x \]

In this form, the y-intercept is the value of \( y \) when \( x = 0 \).

From the equation \( y = -9 - 9x \):

When \( x = 0 \): \[ y = -9 - 9(0) = -9 \]

Thus, the y-intercept is \( -9 \).

As an ordered pair, the y-intercept is:

\[ (0, -9) \]

So the y-intercept is \( (0, -9) \).

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