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

Question

7 x minus 3 y equals 7
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Part 1
yequals
  
enter your response here
​(Simplify your answer. Use integers or fractions for any numbers in the​ expression.)
Part 2
Use a graphing calculator to graph the equation with a standard window. Choose the correct graph below.
A.

A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 1. A line rises from left to right, passing through the points (0, negative 2.3) and (1, 0.0). All coordinates are approximate.
B.

A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 1. A line falls from left to right, passing through the points (0, negative 1.0) and (1, negative 1.4). All coordinates are approximate.
C.

A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 1. A line rises from left to right, passing through the points (0, 1.0) and (1, 1.4). All coordinates are approximate.
D.

Answer 1

To solve for \( y \) in the equation \( 7x - 3y = 7 \), we can rearrange the equation as follows:

1. Isolate the term with \( y \): \[ -3y = 7 - 7x \]

2. Divide by -3 to solve for \( y \): \[ y = \frac{7 - 7x}{-3} \] \[ y = -\frac{7}{3} + \frac{7}{3}x \] \[ y = \frac{7}{3}x - \frac{7}{3} \]

This gives us the equation in slope-intercept form, \( y = mx + b \), where:

• \( m = \frac{7}{3} \) (the slope)
• \( b = -\frac{7}{3} \) (the y-intercept)

Part 1 - Final Answer

Thus, the final answer for \( y \) is: \[ y = \frac{7}{3}x - \frac{7}{3} \]

Part 2 - Graphing

To identify the correct graph based on \( y = \frac{7}{3}x - \frac{7}{3} \):

• The slope \( \frac{7}{3} \) indicates that the line rises as \( x \) increases. Since the y-intercept is a negative value \( -\frac{7}{3} \) (approximately -2.33), the line crosses the y-axis below zero.

From the descriptions of the graphs:

• Graph A shows a line that rises from left to right and passes through the approximate coordinates (0, -2.3) and (1, 0.0), which aligns with the slope and y-intercept we've calculated.

Thus, the correct graph is A.