Question

Graph the equation 9 - x = 3/2y using slope-intercept form.
A. (0, 3), (4, 2)
B. (0, 6), (3, 4)
C. (2, 1), (0, 0)
D. (7, -1), (0, -3)

Answer 1

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:

1. Add \(x\) to both sides:

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

2. Subtract \(x\) from both sides:

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

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

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

4. 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:

1. The y-intercept occurs when \(x = 0\):
\[
y = 6 \quad \text{(Point: (0, 6))}
\]

2. 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)**.