Question 1210484
It looks like you want to **graph two lines** and determine if the point $(6, 1)$ lies on their intersection.

The first equation, $y = -2/3 + 5$, is simply a horizontal line since it's a constant value. The second equation, $-2x + 4y = -8$, is a linear equation in standard form.

Let's first clarify and re-write the equations for graphing.

## 1. Analyze and Simplify the Equations

### Equation 1: $y = -2/3 + 5$

This equation simplifies to a single constant:
$$y = -\frac{2}{3} + \frac{15}{3}$$
$$y = \frac{13}{3} \approx 4.33$$
This is a **horizontal line** where every point has a y-coordinate of $\frac{13}{3}$.

### Equation 2: $-2x + 4y = -8$

It's easiest to graph this line using the slope-intercept form ($y = mx + b$).

1.  **Isolate $y$:**
    $$4y = 2x - 8$$
2.  **Divide by 4:**
    $$y = \frac{2}{4}x - \frac{8}{4}$$
    $$y = \frac{1}{2}x - 2$$
    This line has a **y-intercept ($b$) of $-2$** and a **slope ($m$) of $\frac{1}{2}$** (up 1, right 2).

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## 2. Graphing the Lines

To graph these lines, you'll plot points and draw the lines on a coordinate plane.

### Line 1: $y = \frac{13}{3}$

1.  **Plot the y-intercept:** $(\mathbf{0, \frac{13}{3}})$ or $(0, 4.33)$.
2.  **Draw a horizontal line** passing through that point.
    * Example points: $(3, \frac{13}{3})$, $(-3, \frac{13}{3})$.

### Line 2: $y = \frac{1}{2}x - 2$

1.  **Plot the y-intercept:** $(\mathbf{0, -2})$.
2.  **Use the slope** ($m = \frac{1}{2}$) to find other points:
    * From $(0, -2)$, go up 1 and right 2 to find $(\mathbf{2, -1})$.
    * From $(2, -1)$, go up 1 and right 2 to find $(\mathbf{4, 0})$.
3.  **Draw a straight line** through these points.

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## 3. Check the Given Point $(6, 1)$

Finally, let's see if the point $(6, 1)$ lies on **either** line.

### Check Line 1: $y = \frac{13}{3}$
Substitute $y=1$:
$$1 = \frac{13}{3}$$
This is **False**. The point $(6, 1)$ is **not** on Line 1.

### Check Line 2: $y = \frac{1}{2}x - 2$
Substitute $x=6$ and $y=1$:
$$1 = \frac{1}{2}(6) - 2$$
$$1 = 3 - 2$$
$$1 = 1$$
This is **True**. The point $(6, 1)$ **is** on Line 2.

The point $(6, 1)$ is only on the line $y = \frac{1}{2}x - 2$.

Would you like to find the exact point where these two lines intersect?