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Part 1
Solve for y and graph the equation with a standard window on a graphing utility.
7 x minus 5 y equals 7
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Part 1
yequals
  
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​(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.

1 answer

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.