Question

What is the slope and the y-intercept of the equation 9 + 2/72x= −3/2y. Write the y-intercept as an ordered pair.(1 point)

The slope is ?. The y-intercept is (?).

Answer 1

you sure

Answer 2

To find the slope and the y-intercept of the equation \( 9 + \frac{2}{72}x = -\frac{3}{2}y \), we need to rearrange this equation into the slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

1. Start with the original equation:

\[
9 + \frac{2}{72}x = -\frac{3}{2}y
\]

2. Isolate \( y \) on one side of the equation. First, move \( 9 + \frac{2}{72}x \) to the other side:

\[
-\frac{3}{2}y = -\left(9 + \frac{2}{72}x\right)
\]

3. Multiply through by \(-1\):

\[
\frac{3}{2}y = 9 + \frac{2}{72}x
\]

4. Now, multiply the entire equation by \(\frac{2}{3}\) to solve for \(y\):

\[
y = \frac{2}{3} \cdot 9 + \frac{2}{3} \cdot \frac{2}{72}x
\]

5. Calculate the constants:

\[
y = 6 + \frac{2}{3} \cdot \frac{2}{72}x
\]

To simplify \(\frac{2}{3} \cdot \frac{2}{72}\):

\[
\frac{2 \cdot 2}{3 \cdot 72} = \frac{4}{216} = \frac{1}{54}
\]

So now we can rewrite the equation:

\[
y = 6 + \frac{1}{54}x
\]

Now we have the equation in slope-intercept form \(y = mx + b\), where:

- The slope \(m\) is \(\frac{1}{54}\).
- The y-intercept \(b\) is \(6\), which can be represented as the ordered pair (0, 6).

Thus, we have:

- The slope is \(\frac{1}{54}\).
- The y-intercept is \((0, 6)\).

Final answer:

The slope is \(\frac{1}{54}\). The y-intercept is \((0, 6)\).

Answer 3

Let’s double-check the calculations step-by-step for clarity.

Starting with the original equation:

\[
9 + \frac{2}{72}x = -\frac{3}{2}y
\]

1. Rearrange the equation to isolate \(y\). Start by moving all terms involving \(y\) to one side and the rest to the other side:

\[
-\frac{3}{2}y = -\left(9 + \frac{2}{72}x\right)
\]

Multiplying through by -1 gives:

\[
\frac{3}{2}y = 9 + \frac{2}{72}x
\]

2. Now, divide both sides by \(\frac{3}{2}\) to solve for \(y\):

\[
y = \frac{2}{3} \left(9 + \frac{2}{72}x \right)
\]

3. Distribute \(\frac{2}{3}\):

\[
y = \frac{2}{3} \cdot 9 + \frac{2}{3} \cdot \frac{2}{72}x
\]

Calculating \(\frac{2}{3} \cdot 9\):

\[
\frac{2}{3} \cdot 9 = 6
\]

Now, calculate \(\frac{2}{3} \cdot \frac{2}{72}\):

\[
\frac{2}{3} \cdot \frac{2}{72} = \frac{4}{216} = \frac{1}{54}
\]

Thus, we get:

\[
y = 6 + \frac{1}{54}x
\]

Now that we have the equation in slope-intercept form \(y = mx + b\), we can identify:

- The slope \(m = \frac{1}{54}\)
- The y-intercept \(b = 6\) (which corresponds to the ordered pair \((0, 6)\))

So the final result is confirmed:

- The slope is \(\frac{1}{54}\).
- The y-intercept is \((0, 6)\).

If you have any further questions or clarifications needed, feel free to ask!