solve for y and graph the equation with a standard window on a graphing utility 4x-3y=4

To solve for \(y\) in the equation \(4x - 3y = 4\), follow these steps:

### 1. Solve for \(y\):
Start with the given equation:
\[
4x - 3y = 4
\]

1. Subtract \(4x\) from both sides to isolate the \(y\) term:
   \[
   -3y = 4 - 4x
   \]

2. Divide both sides of the equation by \(-3\) to solve for \(y\):
   \[
   y = \frac{4 - 4x}{-3}
   \]
   Simplifying further:
   \[
   y = \frac{-4x + 4}{-3} \quad \text{or} \quad y = \frac{4x - 4}{3}
   \]

Thus, the equation solved for \(y\) is:
\[
y = \frac{4x - 4}{3}
\]

### 2. Graph the Equation:
To graph this linear equation, note that it is in the slope-intercept form \(y = mx + b\), where:
- Slope (\(m\)) = \(\frac{4}{3}\)
- y-intercept (\(b\)) = \(-\frac{4}{3}\)

Using a standard window on a graphing utility (e.g., \(x\) and \(y\) values ranging from \(-10\) to \(10\)):

1. **y-intercept**: The graph will cross the \(y\)-axis at \(-\frac{4}{3}\) (or approximately \(-1.33\)).
2. **Slope**: From the y-intercept, go up 4 units and to the right 3 units to plot the next point, as the slope is \(\frac{4}{3}\).

Would you like me to generate a visual graph for you?

Here are five related questions:
1. How do you find the x-intercept of the equation \(4x - 3y = 4\)?
2. What does the slope \(\frac{4}{3}\) indicate about the steepness and direction of the line?
3. How would the graph change if the equation were \(4x - 3y = 10\)?
4. How can you rewrite the equation in point-slope form?
5. How do parallel and perpendicular lines relate to the given equation?

**Tip:** When graphing a line, finding both intercepts (x and y) can help quickly sketch the graph without needing to plot multiple points.

Learn how to solve the equation 4x - 3y = 4 to find the value of y and graph the resulting linear equation. This problem covers key concepts in algebra, including solving linear equations and graphing using slope-intercept form. Suitable for students in Grades 7-9.

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