Question

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

Answer 1

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

1. Start with the original equation:

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

2. Rearrange it to isolate \(y\):

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

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

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

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

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

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

5. Identify the slope and y-intercept:
- Slope \(m = -\frac{2}{3}\)
- Y-intercept \(b = 6\)

6. Plot the y-intercept on the graph at \((0, 6)\).

7. From the y-intercept, use the slope to find another point. The slope \(-\frac{2}{3}\) means that for every 3 units you move to the right (positive direction on the x-axis), you move 2 units down (negative direction on the y-axis).

Starting from the point \((0, 6)\):
- Move 3 units right to \(x = 3\),
- Move 2 units down to \(y = 4\).

So, another point is \((3, 4)\).

8. You can also find another point by moving in the opposite direction:
- From \((0, 6)\), move 3 units left to \(x = -3\),
- Move 2 units up to \(y = 8\),

So, another point is \((-3, 8)\).

9. Now you can draw the line through the points \((0, 6)\), \((3, 4)\), and \((-3, 8)\).

By connecting these points, you will graph the line representing the equation \(9 - x = \frac{3}{2}y\).