Question
Solve for y and graph the equation with a standard window on a graphing utility.
9 x minus 2 y equals 9
9 x minus 2 y equals 9
Answers
GPT-4o mini
To solve for \( y \) in the equation \( 9x - 2y = 9 \), we can isolate \( y \):
1. Start with the original equation:
\[
9x - 2y = 9
\]
2. Subtract \( 9x \) from both sides:
\[
-2y = -9x + 9
\]
3. Now, divide by \( -2 \) to get \( y \) by itself:
\[
y = \frac{9 - 9x}{2}
\]
or
\[
y = \frac{9}{2} - \frac{9}{2}x
\]
This can be expressed in slope-intercept form \( y = mx + b \), where:
- The slope \( m = -\frac{9}{2} \)
- The y-intercept \( b = \frac{9}{2} \)
### Graphing the Equation
To graph the equation \( y = -\frac{9}{2}x + \frac{9}{2} \):
1. **Y-Intercept**: Start at the point \( (0, \frac{9}{2}) \) or \( (0, 4.5) \).
2. **Slope**: From the y-intercept, use the slope \( -\frac{9}{2} \). From the point \( (0, 4.5) \):
- Move down 9 units (because of the negative slope) and to the right 2 units. This brings you to the point \( (2, -4.5) \).
3. **Draw the line**: Plot these two points and draw a line through them.
### Standard Window
When using a graphing utility, set the window to standard settings (like \( x \) from -10 to 10 and \( y \) from -10 to 10) to ensure the graph is visible.
### Summary
1. The equation solved for \( y \) is:
\[
y = -\frac{9}{2}x + \frac{9}{2}
\]
2. To graph it, plot the y-intercept and use the slope to find another point. Draw the line through these points using the standard viewing window settings of your graphing utility.
1. Start with the original equation:
\[
9x - 2y = 9
\]
2. Subtract \( 9x \) from both sides:
\[
-2y = -9x + 9
\]
3. Now, divide by \( -2 \) to get \( y \) by itself:
\[
y = \frac{9 - 9x}{2}
\]
or
\[
y = \frac{9}{2} - \frac{9}{2}x
\]
This can be expressed in slope-intercept form \( y = mx + b \), where:
- The slope \( m = -\frac{9}{2} \)
- The y-intercept \( b = \frac{9}{2} \)
### Graphing the Equation
To graph the equation \( y = -\frac{9}{2}x + \frac{9}{2} \):
1. **Y-Intercept**: Start at the point \( (0, \frac{9}{2}) \) or \( (0, 4.5) \).
2. **Slope**: From the y-intercept, use the slope \( -\frac{9}{2} \). From the point \( (0, 4.5) \):
- Move down 9 units (because of the negative slope) and to the right 2 units. This brings you to the point \( (2, -4.5) \).
3. **Draw the line**: Plot these two points and draw a line through them.
### Standard Window
When using a graphing utility, set the window to standard settings (like \( x \) from -10 to 10 and \( y \) from -10 to 10) to ensure the graph is visible.
### Summary
1. The equation solved for \( y \) is:
\[
y = -\frac{9}{2}x + \frac{9}{2}
\]
2. To graph it, plot the y-intercept and use the slope to find another point. Draw the line through these points using the standard viewing window settings of your graphing utility.