Question

Look at the graph:
(0, 5), (3, 3), (6, 1)
What is the y-intercept? _____________
What is the slope? _____________
What is the equation of the line in slope-intercept form? ___________
This is a ___________ relationship
Options: y = 5x - 2, - 2/3, (-5, 0), (0, 5), - 5/3, y = - 2/3x + 5, 7, y = 2/3x + 5, non proportional, proportional, y = -32x + 5, (0, 0), y = 5x + 2/3, 0

Answer 1

To determine the y-intercept, slope, and the equation of the line in slope-intercept form for the points (0, 5), (3, 3), and (6, 1), we can follow these steps:

1. **Y-Intercept**:
The y-intercept is the y-value when x is 0. From the point (0, 5), we see that the y-intercept is:
- **Y-Intercept = 5**

2. **Slope**:
The slope (m) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
We can use any two points. Let's use (3, 3) and (0, 5):
\[
m = \frac{3 - 5}{3 - 0} = \frac{-2}{3}
\]

Alternatively, using points (3, 3) and (6, 1):
\[
m = \frac{1 - 3}{6 - 3} = \frac{-2}{3}
\]
So, the slope is:
- **Slope = -\frac{2}{3}**

3. **Equation of the Line in Slope-Intercept Form**:
The slope-intercept form is given by:
\[
y = mx + b
\]
Where \( m \) is the slope and \( b \) is the y-intercept. From our calculations:
- Slope \( m = -\frac{2}{3} \)
- Y-Intercept \( b = 5 \)

Hence, the equation of the line is:
- **Equation = y = -\frac{2}{3}x + 5**

4. **Type of Relationship**:
Since the points do not pass through the origin (0,0) and the slope is negative, the relationship is considered a:
- **Non-Proportional relationship**

Putting everything together:
- Y-Intercept: 5
- Slope: -\frac{2}{3}
- Equation: y = -\frac{2}{3}x + 5
- Type of Relationship: Non-Proportional

Final Answers:
- Y-Intercept: 5
- Slope: -\frac{2}{3}
- Equation: y = -\frac{2}{3}x + 5
- This is a non-proportional relationship.