To determine which graph correctly represents the equation [tex]\( y = \frac{1}{2} x + 2 \)[/tex], we need to understand what the equation of this line tells us.
1. Identify the slope and y-intercept:
- The equation is written in the slope-intercept form, [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- In this equation, [tex]\( y = \frac{1}{2} x + 2 \)[/tex], the slope ([tex]\( m \)[/tex]) is [tex]\( \frac{1}{2} \)[/tex].
- The y-intercept ([tex]\( b \)[/tex]) is 2.
2. Graph the y-intercept:
- The y-intercept is the point where the graph crosses the y-axis. For this equation, the y-intercept is 2. This means the point (0, 2) is on the graph.
3. Use the slope to find another point:
- The slope [tex]\( \frac{1}{2} \)[/tex] means that for every 2 units you move horizontally (to the right), you move 1 unit vertically (upwards).
- Starting from the y-intercept (0, 2):
- Move 2 units to the right to (2, 2).
- Move 1 unit up to (2, 3).
4. Plot the points:
- Plot the points (0, 2) and (2, 3) on the graph.
- These points will help us draw the line.
5. Draw the line:
- Draw a straight line passing through both points (0, 2) and (2, 3). This is the graph of [tex]\( y = \frac{1}{2} x + 2 \)[/tex].
So, the correct graph representing the equation [tex]\( y = \frac{1}{2} x + 2 \)[/tex] will be the one that has a line passing through the points (0, 2) and (2, 3).
The graphical representation should show a line starting at (0, 2) and rising to the right with a slope of [tex]\( 1/2 \)[/tex]. Make sure to carefully review the graphs provided in the multiple-choice options to find the one that fits these criteria.
