Graph the equation 9−x=32y

Question

using slope-intercept form.(1 point)
Responses

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.

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.

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 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.

Answer 1

To graph the equation \(9 - x = 32y\) in slope-intercept form, we first need to rearrange the equation to isolate \(y\).

Starting with the equation:

\[ 9 - x = 32y \]

1. Rearranging the equation:

   \[ 32y = 9 - x \]

   \[ y = \frac{9 - x}{32} \]

   This can be rewritten as:

   \[ y = -\frac{1}{32}x + \frac{9}{32} \]

From this equation, we see that the slope (\(m\)) is \(-\frac{1}{32}\) and the y-intercept (\(b\)) is \(\frac{9}{32}\).

2. Finding the points to plot:
   • The y-intercept occurs when \(x = 0\): \[ y = \frac{9}{32} \approx 0.28 \quad (\text{approximately}) \]
   • To find another point, we can choose \(x = 32\) to make the calculations easier: \[ y = -\frac{1}{32}(32) + \frac{9}{32} = -1 + \frac{9}{32} \approx -\frac{32}{32} + \frac{9}{32} = -\frac{23}{32} \approx -0.72 \quad (\text{approximately}) \]

Now we have two approximate points: \((0, 0.28)\) and \((32, -0.72)\).

3. Selecting from the responses: Looking at the responses provided, the closest line corresponds to a downward slant and appears to include points less than those we calculated; however, it must also fit the slope of the equation.

The valid response that most closely aligns with the slope-intercept form graph for \(9 - x = 32y\) is likely the one where the coordinates are similar and follow a downward trend through the plotted points.

Given that the slopes provided are negative, the likely candidate from the descriptions is:

An illustration shows a coordinate plane with a downward slanting line passing through (\(0, 6\)) and (\(3, 4\)).

This reflects an overall negative slope even though the specific numerical details of \(y\)-intercepts might differ in exact calculation. Adjust accordingly in graphical understanding.