You are tasked to graphing the equation

Question

𝑦
=
−
4
13
𝑥

+

9
y=
13
−4
​
x + 9 Click Here for Help Video

Our initial point (the y-intercept) is the point is (
,
)

To plot a 2nd point we would start at our initial point and go down
−
4
−4 and right
13
13 and this is the point (
,
)

Answer 1

Let's analyze the equation given:

The equation \( y = -\frac{4}{13}x + 9 \) is in slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Step 1: Identify the y-intercept

The y-intercept \( b \) is 9. This means the initial point (the y-intercept) is: \[ (0, 9) \]

Step 2: Identify the slope

The slope \( m \) is \( -\frac{4}{13} \). This means that for every 13 units you move to the right (positive x-direction), you move down 4 units (negative y-direction).

Step 3: Plot the second point

Starting from the y-intercept \( (0, 9) \):

1. Move down 4 units: \( 9 - 4 = 5 \), so the y-coordinate becomes \( 5 \).
2. Move right 13 units: \( 0 + 13 = 13 \), so the x-coordinate becomes \( 13 \).

Thus, the second point is: \[ (13, 5) \]

Summary of Points

• The initial point (y-intercept) is \( (0, 9) \).
• The second point is \( (13, 5) \).

You can now plot these two points on a graph and draw a line through them to represent the equation \( y = -\frac{4}{13}x + 9 \).