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

6 x minus 5 y equals 6
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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 1.2) 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 rises from left to right, passing through the points (0, 1.0) and (1, 1.8). 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 1.8). All coordinates are approximate.
D.

1 answer

To solve for \( y \) in the equation \( 6x - 5y = 6 \), we can rearrange the equation.

Starting with: \[ 6x - 5y = 6 \]

  1. Move \( 6x \) to the right side: \[ -5y = 6 - 6x \]

  2. Divide everything by \(-5\) to isolate \( y \): \[ y = \frac{6 - 6x}{-5} \] \[ y = -\frac{6}{5} + \frac{6}{5}x \] \[ y = \frac{6}{5}x - \frac{6}{5} \]

This gives us the equation \( y = \frac{6}{5}x - \frac{6}{5} \).

Part 1:

Thus, the simplified equation for \( y \) is: \[ y = \frac{6}{5}x - \frac{6}{5} \]

Part 2:

Now, to graph the equation \( y = \frac{6}{5}x - \frac{6}{5} \), we consider the slope \( \frac{6}{5} \) and y-intercept \( -\frac{6}{5} \) (which is approximately -1.2).

Using a standard window on a graphing utility, we would look for a graph that:

  • Has a line with a positive slope.
  • Passes through the point \( (0, -1.2) \) corresponding to the y-intercept.

Of the given options:

  • A has a point at \( (0, -1.2) \) and rises from left to right, which matches our equation.
  • B and C do not match.
  • D is unspecified but is not listed, so we assume it does not match either.

Conclusion:

The correct graph corresponding to the equation \( y = \frac{6}{5}x - \frac{6}{5} \) is:

A.