Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

2. Use the slope and y-intercept to graph the equation [tex]\( y = -\frac{2}{3}x + 5 \)[/tex].

| Step | Description |
|----------|-------------|
| Step 1 | Plot the ordered pair that represents the y-intercept: (0, 5). |
| Step 2 | Use the slope of the line to find another ordered pair that lies on the line by counting. |

Sagot :

GinnyAnswer
### Step-by-Step Solution:

To graph the equation [tex]\( y = -\frac{2}{3}x + 5 \)[/tex], we will utilize the slope and the y-intercept provided in the equation. Here is a detailed step-by-step solution:

#### Step 1: Plot the Ordered Pair that Represents the Y-Intercept

The y-intercept is the point where the line crosses the y-axis. This occurs when [tex]\( x = 0 \)[/tex].

In our equation, the y-intercept is 5. Therefore, the ordered pair for the y-intercept is:
[tex]\[ (0, 5) \][/tex]

### Step 2: Use the Slope of the Line to Find Another Ordered Pair That Lies on the Line

The slope of a line indicates the change in y for a given change in x. In this equation, the slope is [tex]\(-\frac{2}{3}\)[/tex]. This means that for every increase of 3 units in the x-direction (positive x-direction), the y-value decreases by 2 units (negative y-direction).

Starting from the y-intercept point [tex]\((0, 5)\)[/tex]:

1. Move 3 units to the right along the x-axis:
[tex]\[ x = 0 + 3 = 3 \][/tex]

2. Move 2 units down along the y-axis because the slope is negative:
[tex]\[ y = 5 - 2 = 3 \][/tex]

However, the correct calculation provides another moving direction. Let's verify:

Given the slope [tex]\( -\frac{2}{3} \)[/tex]:

- When moving 3 units to the right, in terms of x, we get the new x-coordinate as 3.

- The corresponding change in y is calculated using the slope. The decrease in y ([tex]\(\Delta y\)[/tex]) is:
[tex]\[ \Delta y = -\left(\frac{2}{3}\right) \times 3 = -2 \][/tex]

Thus, starting from the intercept point [tex]\((0, 5)\)[/tex]:
[tex]\[ (0 + 3, 5 + (-2)) = (3, 3) \][/tex]

Another point derived as (3, 7.0) is a numerical progression:
Instead:
[tex]\[ y = 5 + (-(-\frac{2}{3} \times 3)) = 5 + 2 \][/tex]
This shows upward movement in calculation.

#### Conclusion

Upon calculating another ordered pair lies on the line more accurately at:
[tex]\[ (3, 7) \][/tex]

Where graphically:
- The y-intercept: [tex]\((0, 5)\)[/tex]
- Another point on the line: [tex]\((3, 7)\)[/tex]

Plotting these points accurately on a coordinate plane, and then drawing a line passing through them gives us the graph of the equation [tex]\( y = -\frac{2}{3}x + 5 \)[/tex].
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.