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To solve the problem, we need to first rewrite the given equation in the slope-intercept form \( y = mx + b \), and then graph it.

The given equation is:
\[
1.6x + 1.2y = 5.0
\]

### Step 1: Solve for \( y \) to rewrite in slope-intercept form.
We want to isolate \( y \) on one side of the equation.

1. Subtract \( 1.6x \) from both sides:
\[
1.2y = 5.0 - 1.6x
\]

2. Divide both sides by \( 1.2 \) to solve for \( y \):
\[
y = \frac{5.0 - 1.6x}{1.2}
\]

3. Simplify the right-hand side:
\[
y = \frac{5.0}{1.2} - \frac{1.6x}{1.2}
\]
\[
y = 4.167 - 1.333x
\]

Thus, the equation in slope-intercept form is:
\[
y = -1.333x + 4.167
\]

### Step 2: Graph the equation using the window
The window indicated is \([ -6, 6 ]\) for \(x\) and \([ -4, 4 ]\) for \(y\).

- The slope is \( m = -1.333 \), meaning for every unit increase in \(x\), \(y\) decreases by 1.333 units.
- The \(y\)-intercept is \( b = 4.167 \), meaning the graph crosses the \(y\)-axis at \(y = 4.167\).

To graph the line, plot the intercept at \( (0, 4.167) \), and then use the slope to determine another point. For example, when \(x = 1\), \(y = 4.167 - 1.333 \approx 2.834\). You can plot this and other points based on the slope, and then connect them to form the line.

Would you like further details on graphing this equation or have other questions?

### Related Questions:
1. What is the significance of the slope in a linear equation?
2. How do you determine if a graph has a positive or negative slope based on its equation?
3. What other forms can a linear equation take besides slope-intercept form?
4. How do you graph a line when given only two points?
5. How can you check if a point lies on the line represented by the equation?

### Tip:
Always check the scale of your graphing window to ensure your line fits correctly within the specified ranges.

Write the following equation in the form y = mx + b. Then, using a calculator, graph the line in the window indicated: 1.6x + 1.2y = 5.0, [ -4, 4] by [-6, 6].

Learn how to convert the equation 1.6x + 1.2y = 5.0 into slope-intercept form y = mx + b, and graph it within the specified window. This problem involves key algebraic concepts, including slope and y-intercept calculation, suitable for students in Grades 9-12.

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