To find the x-intercept and y-intercept of the line given by the equation:

$6x - 7y = 42$

We can approach the solution as follows:

1. Find the y-intercept:

The y-intercept occurs where $x = 0$. Substitute $x = 0$ into the equation:

$6(0) - 7y = 42$ $-7y = 42$ $y = -6$

So, the y-intercept is $(0, -6)$.

2. Find the x-intercept:

The x-intercept occurs where $y = 0$. Substitute $y = 0$ into the equation:

$6x - 7(0) = 42$ $6x = 42$ $x = 7$

So, the x-intercept is $(7, 0)$.

Final Answer:

• y-intercept: $y = -6$
• x-intercept: $x = 7$

Let me know if you want more details or have any questions!

Here are 5 related questions for further practice:

1. How do you find the slope of a line given its equation in standard form?
2. Can you express this line in slope-intercept form?
3. What is the equation of a line parallel to this one but passing through a different point?
4. How do you find the x- and y-intercepts for a quadratic equation?
5. How would the intercepts change if the equation were $6x - 7y = -42$?

Tip: When looking for intercepts, remember that the x-intercept is where $y = 0$ and the y-intercept is where $x = 0$.