Question

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

y=−
2
3​x+6



Begin with
b,the y-intercept:

Type the number only. Do NOT enter a coordinate.

Submit
Move with
m,the slope:

GPT-4o mini
For the equation \( y = -\frac{2}{3}x + 6 \):

1. **Y-Intercept (b)**: The y-intercept is found at the constant term in the equation, which is \( 6 \).

2. **Slope (m)**: The slope is the coefficient of \( x \), which is \( -\frac{2}{3} \).

To summarize:
- Y-Intercept (b): **6**
- Slope (m): **-\(\frac{2}{3}\)**

Now to graph the equation:
- Start at the y-intercept (0, 6) on the graph.
- From that point, use the slope to move down 2 units and right 3 units to find another point.
- Repeat to plot more points and draw a line through them to represent the equation.

If you need any more help with the graphing process or have questions on related concepts, feel free to ask!
the points are (0, 0) (1, 1)
GPT-4o mini
The points (0, 0) and (1, 1) do not satisfy the equation \( y = -\frac{2}{3}x + 6 \).

To clarify, the correct points on the graph of the equation are generated based on the slope and y-intercept we identified:

1. **Y-Intercept (b)**: At \( x = 0 \), \( y = 6 \). So, one point is (0, 6).

2. **Using the slope (m)**: The slope is \( -\frac{2}{3} \), which means for every 3 units you move to the right (positive \( x \)), you move 2 units down (negative \( y \)).

Here's how to calculate more points:

- Starting at the y-intercept (0, 6):

- For \( x = 3 \):
\[
y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4
\]
So, the point is (3, 4).

- For \( x = 6 \):
\[
y = -\frac{2}{3}(6) + 6 = -4 + 6 = 2
\]
So, the point is (6, 2).

If you plug in other \( x \) values like 0, 3, or 6 into the equation, you'll get valid points on the graph.

The points (0, 0) and (1, 1) are not on the line represented by your equation, but instead are on the line described by the equation \( y = x \), which does not match \( y = -\frac{2}{3}x + 6 \).

If you have any specific questions or need further assistance, feel free to ask!
what is the y intercept and the slope
GPT-4o mini
For the linear equation \( y = -\frac{2}{3}x + 6 \):

- **Y-Intercept (b)**: The y-intercept is the value of \( y \) when \( x = 0 \). From the equation, this is \( 6 \).

- **Slope (m)**: The slope is the coefficient of \( x \) in the equation. In this case, it is \( -\frac{2}{3} \).

To summarize:
- Y-Intercept (b): **6**
- Slope (m): **-\(\frac{2}{3}\)**
what are the points
GPT-4o mini
To find specific points on the line described by the equation \( y = -\frac{2}{3}x + 6 \), you can choose various values for \( x \) and calculate the corresponding \( y \) values. Here are a few points:

1. **When \( x = 0 \)**:
\[
y = -\frac{2}{3}(0) + 6 = 6
\]
Point: **(0, 6)**

2. **When \( x = 3 \)**:
\[
y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4
\]
Point: **(3, 4)**

3. **When \( x = 6 \)**:
\[
y = -\frac{2}{3}(6) + 6 = -4 + 6 = 2
\]
Point: **(6, 2)**

4. **When \( x = 9 \)**:
\[
y = -\frac{2}{3}(9) + 6 = -6 + 6 = 0
\]
Point: **(9, 0)**

5. **When \( x = -3 \)**:
\[
y = -\frac{2}{3}(-3) + 6 = 2 + 6 = 8
\]
Point: **(-3, 8)**

### Summary of Points
- **(0, 6)**
- **(3, 4)**
- **(6, 2)**
- **(9, 0)**
- **(-3, 8)**

You can plot these points on a graph and draw a line through them to represent the linear equation \( y = -\frac{2}{3}x + 6 \). If you need further assistance, feel free to ask!
what is the x point
GPT-4o mini
To find the x-intercept of the equation \( y = -\frac{2}{3}x + 6 \), you will set \( y \) to 0 and solve for \( x \).

### Setting \( y = 0 \):
\[
0 = -\frac{2}{3}x + 6
\]

### Solving for \( x \):
1. Add \(\frac{2}{3}x\) to both sides:
\[
\frac{2}{3}x = 6
\]

2. Multiply both sides by \(\frac{3}{2}\) to isolate \( x \):
\[
x = 6 \times \frac{3}{2} = 9
\]

Thus, the x-intercept is at the point **(9, 0)**.

### Summary:
- **X-Intercept**: **9** (the coordinate point is (9, 0)).