To find the x-intercept and y-intercept of the given line, we need to follow these steps. The equation provided is:

$7x - 6y = 42$

1. Finding the x-intercept:

The x-intercept is the point where the line crosses the x-axis. At this point, $y = 0$.

Substitute $y = 0$ into the equation:

$7x - 6(0) = 42$

Simplify:

$7x = 42$

Now, solve for $x$:

$x = \frac{42}{7} = 6$

Thus, the x-intercept is $(6, 0)$.

2. Finding the y-intercept:

The y-intercept is the point where the line crosses the y-axis. At this point, $x = 0$.

Substitute $x = 0$ into the equation:

$7(0) - 6y = 42$

Simplify:

$-6y = 42$

Now, solve for $y$:

$y = \frac{42}{-6} = -7$

Thus, the y-intercept is $(0, -7)$.

Conclusion:

• x-intercept: $(6, 0)$
• y-intercept: $(0, -7)$

Would you like a more detailed explanation of any part of the solution?

Here are some related questions for further exploration:

1. How do we find the slope of the given line from the equation?
2. Can we rewrite the equation in slope-intercept form?
3. How do x- and y-intercepts help in graphing a line?
4. What would change if the equation were multiplied by a constant?
5. Can we use another method to verify the intercepts?

Tip: When finding intercepts, always remember that for the x-intercept, set $y = 0$, and for the y-intercept, set $x = 0$.