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

Question

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 \(9 - x = 32y\) in slope-intercept form, we first need to convert it into the appropriate format \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Starting with the given equation: \[ 9 - x = 32y \]

Let's isolate \(y\):

1. Rearrange the equation to get \(32y\) alone on one side: \[ 32y = 9 - x \]

2. Divide every term by 32 to solve for \(y\): \[ y = \frac{9}{32} - \frac{1}{32}x \]

Now we can rewrite this as: \[ y = -\frac{1}{32}x + \frac{9}{32} \]

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

Plotting the Line

To plot the line, start at the y-intercept (\(0, \frac{9}{32}\)). Since \(\frac{9}{32}\) is approximately \(0.28125\), you can estimate this point on the y-axis.

Next, use the slope \(-\frac{1}{32}\):

• For every increase of 32 units in \(x\), \(y\) decreases by 1 unit.

Example Points

1. Y-Intercept: (0, \(0.28125\))
2. Another Point: Move 32 units to the right (to \(x = 32\)), and decrease \(y\) by 1: \[ (32, 0.28125 - 1) = (32, -0.71875) \]

These two points can be used to draw the line.

Conclusion

Choose the graph that accurately reflects these calculations and includes points around (0, 0.28125) and (32, -0.71875). Based on the provided responses, make sure the coordinates of the plotted points adhere to a similar pattern as determined.