To find the coordinates for the line $y = \frac{1}{2}x + 1$ when $x$ takes the values $-4$, $-2$, $0$, and $2$, substitute each $x$-value into the equation and solve for $y$.

Step-by-step calculation:

1. For $x = -4$: $y = \frac{1}{2}(-4) + 1 = -2 + 1 = -1$ Coordinate: $(-4, -1)$

2. For $x = -2$: $y = \frac{1}{2}(-2) + 1 = -1 + 1 = 0$ Coordinate: $(-2, 0)$

3. For $x = 0$: $y = \frac{1}{2}(0) + 1 = 0 + 1 = 1$ Coordinate: $(0, 1)$

4. For $x = 2$: $y = \frac{1}{2}(2) + 1 = 1 + 1 = 2$ Coordinate: $(2, 2)$

Final coordinates:

$(-4, -1), (-2, 0), (0, 1), (2, 2)$

Would you like to see these points graphed or explained further?

---

Related Questions:

1. How do you determine the slope of the line $y = \frac{1}{2}x + 1$?
2. What is the y-intercept of $y = \frac{1}{2}x + 1$, and how is it derived?
3. How can we verify that a point lies on the line $y = \frac{1}{2}x + 1$?
4. What are the coordinates for other $x$-values, such as $x = 4$ or $x = -6$?
5. How would the graph of $y = \frac{1}{2}x + 1$ compare to $y = x + 1$?

Tip:

To plot any line, always start with the y-intercept and use the slope to find additional points.