The given equation is:

$3x - 7y = 15$

This is a linear equation in two variables, $x$ and $y$. To explore this equation further, we can perform different operations such as solving for one variable in terms of the other, finding its intercepts, or expressing it in slope-intercept form.

Solving for $y$ (Slope-Intercept Form):

To express the equation in slope-intercept form, which is $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept:

1. Start with: $3x - 7y = 15$

2. Subtract $3x$ from both sides: $-7y = -3x + 15$

3. Divide the entire equation by $-7$: $y = \frac{3}{7}x - \frac{15}{7}$

Now, the equation is in the form $y = \frac{3}{7}x - \frac{15}{7}$, where the slope $m = \frac{3}{7}$ and the y-intercept is $-\frac{15}{7}$.

Would you like further details on graphing or solving this in another way?

Here are some questions that expand on this topic:

1. How do you find the x-intercept of this equation?
2. What is the slope of a line perpendicular to this one?
3. How can you express the equation in standard form?
4. What is the significance of the slope in real-world scenarios?
5. How would the graph of this equation change if the constant term (15) changed?

Tip: When dealing with linear equations, always check if expressing it in different forms (slope-intercept, point-slope, etc.) helps better understand the problem.