You are tasked to graphing the equation y=4/17 +5

Question

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 \( (17, 9) \).