To find the intercepts of the equation $y = -\frac{1}{2}x + 6$, we'll calculate both the x-intercept and the y-intercept separately.

1. 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:

$y = -\frac{1}{2}(0) + 6 = 6$

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

2. X-intercept:

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

Set $y = 0$ in the equation and solve for $x$:

$0 = -\frac{1}{2}x + 6$

Move 6 to the other side:

$-\frac{1}{2}x = -6$

Multiply both sides by -2 to solve for $x$:

$x = 12$

So, the x-intercept is $(12, 0)$.

Final Answer:

• Y-intercept: $(0, 6)$
• X-intercept: $(12, 0)$

Would you like more details or have any questions about this?

Here are some related questions:

1. How do you graph a line given its intercepts?
2. What is the slope of the line, and how does it affect the graph?
3. Can the intercepts be used to write the equation of the line in another form?
4. What happens to the intercepts if we change the slope in the equation?
5. How can we find intercepts of a quadratic equation?

Tip: When finding intercepts, always set the opposite variable to zero (set $x = 0$ for the y-intercept and $y = 0$ for the x-intercept).