Question

Identify the slope and y intercept. Then, graph the linear equation.

`y=-\frac{2}{3}x+5`



Begin with `b,`the y-intercept:

Answer 1

To identify the slope and y-intercept from the equation \( y = -\frac{2}{3}x + 5 \), we can break it down:

1. **Slope (m):** The slope is the coefficient of \( x \) in the equation. For the given equation:
\[
m = -\frac{2}{3}
\]

2. **Y-intercept (b):** The y-intercept is the constant term in the equation. From the equation, we have:
\[
b = 5
\]

Now, we can summarize:

- **Y-intercept:** \( (0, 5) \)
- **Slope:** \( -\frac{2}{3} \)

### Graphing the Equation

1. **Plot the Y-intercept:** Start by plotting the point \( (0, 5) \) on the graph.

2. **Use the Slope:** The slope \( -\frac{2}{3} \) indicates that for every 3 units you move to the right (positive direction on the x-axis), you move down 2 units (negative direction on the y-axis).

3. **Finding another point:** From the y-intercept \( (0, 5) \):
- Move 3 units to the right: \( (0 + 3, 5) \Rightarrow (3, 5) \)
- Then, move down 2 units: \( (3, 5 - 2) \Rightarrow (3, 3) \)

Therefore, another point on the line is \( (3, 3) \).

4. **Draw the line:** Connect the points \( (0, 5) \) and \( (3, 3) \) with a straight line, and extend the line in both directions.

This will give you the graph of the linear equation \( y = -\frac{2}{3}x + 5 \). If you were to visualize it, it would slope downwards from left to right.