To graph the equation \(9 - x = \frac{3}{2}y\), we first need to rewrite it in slope-intercept form \(y = mx + b\).
Starting with the original equation:
\[ 9 - x = \frac{3}{2}y \]
We can isolate \(y\) by rearranging the equation:
- Add \(x\) to both sides:
\[ 9 = x + \frac{3}{2}y \]
- Subtract \(x\) from both sides:
\[ 9 - x = \frac{3}{2}y \]
- Now, multiply both sides by \(\frac{2}{3}\) to solve for \(y\):
\[ y = \frac{2}{3}(9 - x) \]
- Distributing \(\frac{2}{3}\):
\[ y = 6 - \frac{2}{3}x \]
So, in slope-intercept form, the equation is:
\[ y = -\frac{2}{3}x + 6 \]
Here, the slope \(m\) is \(-\frac{2}{3}\), and the y-intercept \(b\) is \(6\).
Next, let's find two points that satisfy this equation to help with graphing:
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The y-intercept occurs when \(x = 0\): \[ y = 6 \quad \text{(Point: (0, 6))} \]
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Now let's find another point by substituting a value for \(x\). Let’s choose \(x = 3\): \[ y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \quad \text{(Point: (3, 4))} \]
Now we can plot the points (0, 6) and (3, 4).
Looking at the options provided:
A. (0, 3), (4, 2)
B. (0, 6), (3, 4)
C. (2, 1), (0, 0)
D. (7, -1), (0, -3)
The correct answer is B. (0, 6), (3, 4).