Graph the equation 9−x=32y

Question

Graph the equation 9−x=32y
 using slope-intercept form.(1 point)
Responses

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 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.

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.
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GPT-4o mini · Answer

To graph the equation $ 9 - x = 32y $ using slope-intercept form, we first need to rearrange the equation into the standard slope-intercept form, which is $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept. Starting from the original equation: $$ 9 - x = 32y $$ 1. Rearrange it to isolate $ y $: $$ 32y = 9 - x $$ $$ 32y = -x + 9 $$ 2. Divide by 32 to solve for $ y $: $$ y = -\frac{1}{32}x + \frac{9}{32} $$ Now we have the equation in slope-intercept form $ y = mx + b $: - Slope ($ m $): $ -\frac{1}{32} $ - Y-intercept ($ b $): $ \frac{9}{32} $ To graph this line: 1. **Plot the y-intercept**: The y-intercept $\frac{9}{32}$ approximates to $0.28125$, so you can plot the point (0, 0.28125) on the y-axis. 2. **Use the slope to find another point**: The slope of $-\frac{1}{32}$ means that for every 32 units you move to the right on the x-axis, you move down 1 unit on the y-axis. So from (0, $0.28125$), if you move 32 units to the right (to $x = 32$), you will move down 1 unit to $y = 0.28125 - 1 = -0.71875$. Therefore, you can plot the point (32, -0.71875). 3. **Draw the line**: Connect the plotted points and extend the line in both directions. Given the visual options you've described, the graph resembling a downward slanting line between the points provided in the options could be similar to the equation we graphed, particularly if it reflects a negative slope and starts from near (0, 0.28125). Based on the details from the problem statement, the most relevant graph would be the one that has points that resemble the slope of -1/32 and intersects at a positive y-value. Since none of the options provided exactly matches those calculations directly, the correct choice may depend on a closest approximation among the provided images. If there are specific coordinates listed in the images, those should be compared for closest alignment with the line you graphed.