Question

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

A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma 3 right parenthesis, and left parenthesis 4 comma 2 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma 3 right parenthesis, and left parenthesis 4 comma 2 right parenthesis.

A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 2 comma 1 right parenthesis.
Image with alt text: A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 2 comma 1 right parenthesis.

A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 3 right parenthesis, and left parenthesis 7 comma negative 1 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 3 right parenthesis, and left parenthesis 7 comma negative 1 right parenthesis.

An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. A downward slanting line is graphed on the coordinate plane. The downward slanting line passes through closed points plotted at left parenthesis 0 comma 6 right parenthesis and left parenthesis 3 comma 4 right parenthesis.
Image with alt text: An illustration shows a coordinate plane with four quadrants. The x and y axes range from negative 10 to 10 in one unit increments. A downward slanting line is graphed on the coordinate plane. The downward slanting line passes through closed points plotted at left parenthesis 0 comma 6 right parenthesis and left parenthesis 3 comma 4 right parenthesis.
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Answer 1

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

Starting with the original equation:

1. Rearrange the equation to isolate \(y\):
\[
9 - x = \frac{3}{2}y
\]
Adding \(x\) to both sides gives:
\[
9 = \frac{3}{2}y + x
\]
Subtracting \(x\) from both sides gives:
\[
9 - x = \frac{3}{2}y
\]

2. Now, multiply both sides by \(\frac{2}{3}\) to solve for \(y\):
\[
y = \frac{2}{3}(9 - x)
\]

Distributing gives:
\[
y = \frac{18}{3} - \frac{2}{3}x
\]
Simplifying:
\[
y = 6 - \frac{2}{3}x
\]

Now we have the equation in slope-intercept form:
\[
y = -\frac{2}{3}x + 6
\]
From this equation, we know the slope \(m = -\frac{2}{3}\) and the y-intercept \(b = 6\).

**Finding Points for the Graph:**

1. The y-intercept is \(6\) (point \( (0, 6) \)).
2. To find another point, you can choose any value of \(x\). For example, if \(x = 3\):
\[
y = 6 - \frac{2}{3}(3) = 6 - 2 = 4 \quad \text{(point \( (3, 4) \))}
\]
3. Another example, if \(x = 6\):
\[
y = 6 - \frac{2}{3}(6) = 6 - 4 = 2 \quad \text{(point \( (6, 2) \))}
\]

**Plotting the Points:**
- The points \( (0, 6) \) and \( (3, 4) \) can be plotted on the coordinate plane.
- Draw a line through these points, extending it in both directions.

Choose from the options given based on the plotted points and line:
- Verify the plotted points and the line characteristics. The correct option should have a line that matches the slope and y-intercept calculated.

Based on the information given, it seems the correct response will describe a line that goes through points like \( (0, 6) \) and \( (3, 4) \) or similar points consistent with a downward slope.