Solve for y and graph the equation with a standard window on a graphing utility.

Question

9 x minus 2 y equals 9

Answer 1

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.