Question
Solve for y and graph the equation with a standard window on a graphing utility.
7 x minus 3 y equals 7
Question content area bottom
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.
7 x minus 3 y equals 7
Question content area bottom
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.
Answers
GPT-4o mini
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.**
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.**