Question

Graph the line with the equation y, equals, minus, start fraction, 2, divided by, 3, end fraction, x, plus, 4y=−
3
2
​
x+4.

Answer 1

The equation you provided seems to have a small mix-up, but we can work with it. I will interpret it as the linear equation:

\[
y = -\frac{2}{3}x + 4
\]

To graph this line, we can follow a series of steps:

1. **Identify the slope and the y-intercept**:
- The slope (m) is \(-\frac{2}{3}\).
- The y-intercept (b) is \(4\), which means the line crosses the y-axis at the point \((0, 4)\).

2. **Plot the y-intercept**:
- Start at the origin \((0, 0)\) on the Cartesian plane and move up to \(4\) on the y-axis. Place a point there: \((0, 4)\).

3. **Use the slope to find another point**:
- From the y-intercept \((0, 4)\), use the slope \(-\frac{2}{3}\). This means that for every \(3\) units you move to the right (positive x-direction), you move \(2\) units down (negative y-direction).
- Starting from \((0, 4)\):
- Move \(3\) units to the right to get to \( (3, 4) \).
- Move down \(2\) units to arrive at the point \((3, 2)\).

4. **Plot the second point**:
- Place a point at \((3, 2)\).

5. **Draw the line**:
- Use a ruler to draw a straight line through the two points \((0, 4)\) and \((3, 2)\).

### Additional Points:
To ensure accuracy, you can find more points using the equation:
- If \(x = 0\), then \(y = 4\) (already plotted)
- If \(x = 3\), then \(y = 2\) (already plotted)
- If \(x = -3\), then:
\[
y = -\frac{2}{3}(-3) + 4 = 2 + 4 = 6
\]
So the point \((-3, 6)\) can also be plotted.

You can plot this third point and ensure the line has the correct slope.

### Final Graph:
Once you connect the points, you should have a graph of the line with \( y = -\frac{2}{3}x + 4 \) that accurately represents the relationship defined by the equation. The line will slope downwards from left to right, reflecting the negative slope of \(-\frac{2}{3}\).