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

7 x minus 2 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 falls from left to right, passing through the points (0, negative 1.0) and (1, negative 1.3). 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, 3.5) 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 rises from left to right, passing through the points (0, 1.0) and (1, 1.3). All coordinates are approximate.
D.

1 answer

To solve the equation \(7x - 2y = 7\) for \(y\), we will follow these steps:

  1. Isolate \(y\) on one side of the equation.
  2. Rearranging gives:

\[ 7x - 2y = 7 \implies -2y = -7x + 7 \]

  1. Dividing through by -2 gives:

\[ y = \frac{7}{2} - \frac{7}{2}x \]

Rearranging it gives us:

\[ y = -\frac{7}{2}x + \frac{7}{2} \]

Thus, the solution for \(y\) is:

\[ y = -\frac{7}{2}x + \frac{7}{2} \]

This function describes a linear equation in slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Part 2: Graphing

Now we can graph the equation:

  • The slope \(m = -\frac{7}{2}\) indicates the line falls as you move from left to right.
  • The y-intercept \(b = \frac{7}{2} = 3.5\) indicates where the line crosses the y-axis.

By examining the options provided:

  • A line that falls from left to right is expected, and it should pass through the point (0, 3.5).
  • Therefore, the correct graph is:

B.