Question

You are tasked to graphing the equation y=4/17 +5
Our initial point (the y-intercept) is the point is (

To plot a 2nd point we would start at our initial point and go up
4
4 and right
17
17 and this is the point (
,
)

Answer 1

To graph the equation \( y = \frac{4}{17}x + 5 \), we want to identify the y-intercept and then find another point on the line using the slope.

1. **Identify the y-intercept**: This occurs when \( x = 0 \). Plugging \( x = 0 \) into the equation:

\[
y = \frac{4}{17}(0) + 5 = 5
\]

So the y-intercept is the point \( (0, 5) \).

2. **Find the slope**: The slope of the equation is \( \frac{4}{17} \). This means that for every \( 17 \) units you move to the right (positive \( x \)-direction), you move up \( 4 \) units.

3. **Plot the second point**: Starting from the initial point \( (0, 5) \):
- Move **right** \( 17 \) units: \( 0 + 17 = 17 \)
- Move **up** \( 4 \) units: \( 5 + 4 = 9 \)

So the second point is \( (17, 9) \).

### Summary:
- **The initial point (y-intercept)** is \( (0, 5) \).
- **The second point** is \( (17, 9) \).

Thus, to fill in the blanks in your statement:
- Our initial point (the y-intercept) is the point \( (0, 5) \).

- To plot a 2nd point we would start at our initial point and go up \( 4 \) and right \( 17 \) and this is the point \( (17, 9) \).