Question

solution:
y = 1 + x

y = 2 + \frac{1}{x}

Explanation:

Step1: Identify intercepts for $y=\frac{1}{2}x+2$

y-intercept: when $x=0$, $y=2$ → point $(0,2)$
x-intercept: when $y=0$, $0=\frac{1}{2}x+2$ → $x=-4$ → point $(-4,0)$

Step2: Identify intercepts for $y=x+1$

y-intercept: when $x=0$, $y=1$ → point $(0,1)$
x-intercept: when $y=0$, $0=x+1$ → $x=-1$ → point $(-1,0)$

Step3: Solve for intersection point

Set $\frac{1}{2}x+2 = x+1$
$2-1 = x-\frac{1}{2}x$
$\frac{1}{2}x=1$ → $x=2$
Substitute $x=2$ into $y=x+1$: $y=3$ → point $(2,3)$

Step4: Plot lines on grid

1. For $y=\frac{1}{2}x+2$: connect $(-4,0)$ and $(0,2)$, extend line.
2. For $y=x+1$: connect $(-1,0)$ and $(0,1)$, extend line.
3. Mark intersection $(2,3)$.

Answer:

The two lines intersect at the point $(2, 3)$. To plot:

1. Draw $y=\frac{1}{2}x+2$ through $(-4,0)$ and $(0,2)$
2. Draw $y=x+1$ through $(-1,0)$ and $(0,1)$
3. Label their intersection at $(2,3)$