To plot the graph of the linear function represented by the equation [tex]\( y = \frac{1}{2}x - 2 \)[/tex], we can follow these detailed steps:
1. Identify the slope and y-intercept:
- The equation of the linear function is given as [tex]\( y = \frac{1}{2}x - 2 \)[/tex].
- Here, the slope ([tex]\(m\)[/tex]) is [tex]\( \frac{1}{2} \)[/tex], and the y-intercept ([tex]\(b\)[/tex]) is [tex]\(-2\)[/tex].
2. Determine the y-values for given x-values:
- Choose a set of x-values. A straightforward set might be [tex]\( x = 0, 2, 4, 6, 8, 10 \)[/tex].
- Calculate the corresponding y-values using the equation [tex]\( y = \frac{1}{2}x - 2 \)[/tex].
3. Calculate y-values:
- When [tex]\( x = 0 \)[/tex]:
[tex]\[ y = \frac{1}{2}(0) - 2 = -2.0 \][/tex]
- When [tex]\( x = 2 \)[/tex]:
[tex]\[ y = \frac{1}{2}(2) - 2 = -1.0 \][/tex]
- When [tex]\( x = 4 \)[/tex]:
[tex]\[ y = \frac{1}{2}(4) - 2 = 0.0 \][/tex]
- When [tex]\( x = 6 \)[/tex]:
[tex]\[ y = \frac{1}{2}(6) - 2 = 1.0 \][/tex]
- When [tex]\( x = 8 \)[/tex]:
[tex]\[ y = \frac{1}{2}(8) - 2 = 2.0 \][/tex]
- When [tex]\( x = 10 \)[/tex]:
[tex]\[ y = \frac{1}{2}(10) - 2 = 3.0 \][/tex]
4. Compile the points to plot:
- The pairs of [tex]\((x, y)\)[/tex] values we have are:
- [tex]\( (0, -2.0) \)[/tex]
- [tex]\( (2, -1.0) \)[/tex]
- [tex]\( (4, 0.0) \)[/tex]
- [tex]\( (6, 1.0) \)[/tex]
- [tex]\( (8, 2.0) \)[/tex]
- [tex]\( (10, 3.0) \)[/tex]
5. Plot the graph:
- On a coordinate plane, plot the points:
- [tex]\( (0, -2.0) \)[/tex]
- [tex]\( (2, -1.0) \)[/tex]
- [tex]\( (4, 0.0) \)[/tex]
- [tex]\( (6, 1.0) \)[/tex]
- [tex]\( (8, 2.0) \)[/tex]
- [tex]\( (10, 3.0) \)[/tex]
- Draw a straight line through these points.
The straight line that passes through these points represents the graph of the linear function [tex]\( y = \frac{1}{2}x - 2 \)[/tex].
