To find the intercepts of the line given by the equation $y = 2x + 6$, let's determine both the x-intercept and y-intercept.

1. Finding the y-intercept

The y-intercept occurs when $x = 0$.

$y = 2(0) + 6 = 6$

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

2. Finding the x-intercept

The x-intercept occurs when $y = 0$.

$0 = 2x + 6$

Solving for $x$: $2x = -6$ $x = -3$

So, the x-intercept is at the point $(-3, 0)$.

Conclusion

The intercepts are:

• x-intercept: $(-3, 0)$
• y-intercept: $(0, 6)$

The correct answer choice is:

• A. The intercept(s) is/are $(-3, 0)$ and $(0, 6)$.

Would you like further details or have any questions?

Here are some related questions to explore further:

1. How can you determine the slope of a line from its equation?
2. What is the significance of the slope-intercept form $y = mx + b$?
3. How do intercepts change when you adjust the slope or intercept in an equation?
4. What are the intercepts for a quadratic equation?
5. How do intercepts help in graphing a line?

Tip: To find intercepts, set one variable to zero and solve for the other. This gives you the points where the line crosses the axes.