The equation given is \(-2x + 3y = 14\). To analyze or solve this equation, we have a few options, such as finding the slope-intercept form, solving for one variable in terms of the other, or graphing it.

### 1. **Slope-Intercept Form:**
To rewrite the equation in the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept, follow these steps:

\[
-2x + 3y = 14
\]

Add \(2x\) to both sides:

\[
3y = 2x + 14
\]

Divide by 3:

\[
y = \frac{2}{3}x + \frac{14}{3}
\]

So, the slope-intercept form is:

\[
y = \frac{2}{3}x + \frac{14}{3}
\]

Here, the slope \(m\) is \(\frac{2}{3}\), and the y-intercept \(b\) is \(\frac{14}{3}\).

### 2. **Solving for \(y\) in terms of \(x\):**
If you have a value for \(x\), you can plug it into the equation to find \(y\).

For example, if \(x = 0\):

\[
y = \frac{2}{3}(0) + \frac{14}{3} = \frac{14}{3}
\]

### 3. **Solving for \(x\) in terms of \(y\):**
Similarly, if you have a value for \(y\), you can solve for \(x\):

For example, if \(y = 0\):

\[
0 = \frac{2}{3}x + \frac{14}{3}
\]

Multiply by 3 to eliminate the fraction:

\[
0 = 2x + 14
\]

Subtract 14 from both sides:

\[
-14 = 2x
\]

Divide by 2:

\[
x = -7
\]

### 4. **Graphing the Equation:**
This equation represents a straight line. You can plot the graph using the y-intercept \(\left(0, \frac{14}{3}\right)\) and the slope \(\frac{2}{3}\).

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Would you like more details on any of these methods, or do you have any questions?

### Related Questions:
1. How do you find the x-intercept of a linear equation?
2. What does the slope of a line represent in a real-world context?
3. How can you determine if two lines are parallel?
4. What is the general form of a linear equation?
5. How do you graph a linear equation by finding intercepts?
6. How does changing the slope affect the steepness of a line?
7. What is the significance of the y-intercept in a graph?
8. How can you check if a point lies on the line given by the equation?

**Tip:** When solving linear equations, converting to slope-intercept form makes it easier to identify the slope and y-intercept for graphing.

Learn how to solve the linear equation -2x + 3y = 14 step-by-step. This problem covers key algebraic concepts, including linear equations and the slope-intercept form. Suitable for students in Grades 7-9.

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