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.