9-d=3/2y graph this equation using slope intercept form

Answer 1

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

First, solve the given equation for \( y \):

1. Start with the given equation:
\[ 9 - d = \frac{3}{2}y \]

2. Solving for \( y \):
\[ \frac{3}{2}y = 9 - d \]
\[ y = \frac{2}{3} (9 - d) \]

3. Distributing the \(\frac{2}{3}\):
\[ y = \frac{2}{3} \cdot 9 - \frac{2}{3} \cdot d \]
\[ y = 6 - \frac{2}{3}d \]

Now, we have the equation in slope-intercept form \( y = mx + b \), where \( m = -\frac{2}{3} \) and \( b = 6 \).

To graph this:

1. Plot the y-intercept (\( b \)), which is \( 6 \). This is the point \( (0, 6) \) on the graph.

2. Use the slope \( m = -\frac{2}{3} \) to determine the next points. The slope means for every 3 units you move to the right (positive x direction), you move 2 units down (negative y direction):
- From the y-intercept (0, 6), move 3 units to the right, arriving at (3, 6).
- From there, move 2 units down, arriving at the point (3, 4).

3. Plot the second point (3, 4).

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

This line represents the graph of the equation \( 9 - d = \frac{3}{2}y \).