Question

Graph the equation 9 − x =3/2 y using slope-intercept form. (1 point)

Answer 1

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

Starting with the given equation:

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

We can isolate \( y \) by multiplying both sides by \( \frac{2}{3} \):

\[
\frac{2}{3}(9 - x) = y
\]

Distributing \( \frac{2}{3} \):

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

Now, we can write it in slope-intercept form:

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

From this equation, we can identify:
- The slope \( m = -\frac{2}{3} \)
- The y-intercept \( b = 6 \) (meaning the line crosses the y-axis at (0, 6))

### Steps to Graph:

1. Plot the y-intercept (0, 6).
2. Use the slope to find another point. The slope of \( -\frac{2}{3} \) means that for every 3 units you move to the right (positive x-direction), you move down 2 units (negative y-direction).
3. Starting from (0, 6):
- Move 3 units to the right: (3, 6)
- Move down 2 units: (3, 4)
- Plot the point (3, 4).

4. Draw a line through the points (0, 6) and (3, 4).

### Final Graph:
The line you graphed represents the equation \( y = -\frac{2}{3}x + 6 \), demonstrating the relationship defined by the original equation \( 9 - x = \frac{3}{2} y \).