The image shows a math exercise that asks to graph the function given by the equation $y = \frac{1}{2}x + 1$. The specific x-values provided are $x = -4, -2, 0, 2, 4$.

To Graph the Function

1. Calculate $y$-values for given $x$-values:

   &\text{For } x = -4: & y &= \frac{1}{2}(-4) + 1 = -2 + 1 = -1 \\ &\text{For } x = -2: & y &= \frac{1}{2}(-2) + 1 = -1 + 1 = 0 \\ &\text{For } x = 0: & y &= \frac{1}{2}(0) + 1 = 0 + 1 = 1 \\ &\text{For } x = 2: & y &= \frac{1}{2}(2) + 1 = 1 + 1 = 2 \\ &\text{For } x = 4: & y &= \frac{1}{2}(4) + 1 = 2 + 1 = 3 \\ \end{aligned}$$

2. Plot these points on a graph:

   • $(-4, -1)$
   • $(-2, 0)$
   • $(0, 1)$
   • $(2, 2)$
   • $(4, 3)$

3. Draw the line: Connect the points to visualize the linear function $y = \frac{1}{2}x + 1$.

Would you like more detailed instructions or a graph visualization?

Relative Questions:

1. How do you find the slope of a linear function?
2. What is the significance of the y-intercept in a linear equation?
3. How do you determine if two lines are parallel or perpendicular?
4. What are the steps to convert a linear equation into slope-intercept form?
5. How do changes in the slope and y-intercept affect the graph of a line?

Tip:

When graphing linear equations, start by identifying the y-intercept and use the slope to determine additional points.