Question
Question content area top
Part 1
Solve for y and graph the equation with a standard window on a graphing utility.
7 x minus 5 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 1.4) 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, 1.4) and (1, 0.0). 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 falls from left to right, passing through the points (0, negative 1.0) and (1, negative 1.7). All coordinates are approximate.
D.
Part 1
Solve for y and graph the equation with a standard window on a graphing utility.
7 x minus 5 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 1.4) 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, 1.4) and (1, 0.0). 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 falls from left to right, passing through the points (0, negative 1.0) and (1, negative 1.7). All coordinates are approximate.
D.
Answers
GPT-4o mini
To solve the equation \( 7x - 5y = 7 \) for \( y \):
1. Start by isolating \( y \):
\[
7x - 5y = 7
\]
Subtract \( 7x \) from both sides:
\[
-5y = -7x + 7
\]
Now, divide every term by \(-5\):
\[
y = \frac{7}{5}x - \frac{7}{5}
\]
2. Therefore, the solution for \( y \) is:
\[
y = \frac{7}{5}x - \frac{7}{5}
\]
Now, let's determine how to graph the equation.
### Graphing the Equation
The slope-intercept form of the equation is \( y = mx + b \) where \( m \) is the slope and \( b \) is the y-intercept. In this case, the slope \( m = \frac{7}{5} \) indicates that the line rises from left to right. The y-intercept \( b = -\frac{7}{5} \) indicates that the line crosses the y-axis at \(-1.4\) (since \(-\frac{7}{5} = -1.4\)).
### Identifying the Correct Graph
Now, let's look at the provided options:
- **Graph A** shows a line that rises from left to right, passing through \( (0, -1.4) \) and \( (1, 0.0) \).
- **Graph B** shows a line that falls from left to right.
- **Graph C** shows a line that falls from left to right, but at different y-values than expected.
- **Graph D** does not contain any description.
Since the only graph that represents a line with a positive slope, passing through \( (0, -1.4) \) and confirming the direction of the rise, is Graph **A**.
### Conclusion
1. The value of \( y \) is:
\[
y = \frac{7}{5}x - \frac{7}{5}
\]
2. The correct graph based on the characteristics of the slope and intercept is **Graph A**.
1. Start by isolating \( y \):
\[
7x - 5y = 7
\]
Subtract \( 7x \) from both sides:
\[
-5y = -7x + 7
\]
Now, divide every term by \(-5\):
\[
y = \frac{7}{5}x - \frac{7}{5}
\]
2. Therefore, the solution for \( y \) is:
\[
y = \frac{7}{5}x - \frac{7}{5}
\]
Now, let's determine how to graph the equation.
### Graphing the Equation
The slope-intercept form of the equation is \( y = mx + b \) where \( m \) is the slope and \( b \) is the y-intercept. In this case, the slope \( m = \frac{7}{5} \) indicates that the line rises from left to right. The y-intercept \( b = -\frac{7}{5} \) indicates that the line crosses the y-axis at \(-1.4\) (since \(-\frac{7}{5} = -1.4\)).
### Identifying the Correct Graph
Now, let's look at the provided options:
- **Graph A** shows a line that rises from left to right, passing through \( (0, -1.4) \) and \( (1, 0.0) \).
- **Graph B** shows a line that falls from left to right.
- **Graph C** shows a line that falls from left to right, but at different y-values than expected.
- **Graph D** does not contain any description.
Since the only graph that represents a line with a positive slope, passing through \( (0, -1.4) \) and confirming the direction of the rise, is Graph **A**.
### Conclusion
1. The value of \( y \) is:
\[
y = \frac{7}{5}x - \frac{7}{5}
\]
2. The correct graph based on the characteristics of the slope and intercept is **Graph A**.