Question

Graph the equation 9−x=32y 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.

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.
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 \( 9 - x = 32y \) in slope-intercept form, we need to rearrange the equation into the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Starting with the original equation:

\[
9 - x = 32y
\]

First, isolate \( y \):

\[
32y = 9 - x
\]

Next, divide everything by 32 to solve for \( y \):

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

This simplifies to:

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

Now we can see that:

- The slope \( m = -\frac{1}{32} \)
- The y-intercept \( b = \frac{9}{32} \)

To graph the equation, we start by plotting the y-intercept at \( (0, \frac{9}{32}) \). We can also plot another point using the slope. For every increase of 32 in \( x \), \( y \) will decrease by 1 (since the slope is negative).

Using the slope, we can calculate the coordinates of a second point. Starting at the y-intercept, let's pick an \( x \) value. If \( x = 32 \):

\[
y = -\frac{1}{32}(32) + \frac{9}{32} = -1 + \frac{9}{32} = \frac{9 - 32}{32} = \frac{-23}{32}
\]

Now we have two points:
1. \( (0, \frac{9}{32}) \)
2. \( (32, -\frac{23}{32}) \)

You can continue graphing the line using the identified points.

Among the given options, the correct graph is the one that shows a line with these coordinates correctly represented. If you have the opportunity to match with observed plotted points, then look for points that suggest this downward slope and correspond to the y-intercept found.

If the visual descriptions you've provided do not represent these points correctly, you may need to choose the one that seems closest or has a slope that appears reasonable given the format. Otherwise, you could graph based on my points described above.