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:
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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
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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}
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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
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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.
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