Question

graph the system of equations to deter
$y = \frac{1}{2}x + 3$
$2y = x + 6$
use the graphing tool to graph the syst
click the graph to plot the second point on your line.
(1,3)

Explanation:

Step1: Simplify the second equation

Divide $2y=x+6$ by 2:
$$y=\frac{1}{2}x+3$$

Step2: Identify a second point

Use $x=2$ in $y=\frac{1}{2}x+3$:
$$y=\frac{1}{2}(2)+3=1+3=4$$
This gives the point $(2,4)$.

Step3: Verify consistency

Both equations are identical, so any point on $y=\frac{1}{2}x+3$ works.

Answer:

Plot the point $(2,4)$ (or any other valid point on the line $y=\frac{1}{2}x+3$, such as $(4,5)$ or $(-2,2)$) to complete the line. The system has infinitely many solutions since the two equations represent the same line.