To provide accurate answers to your questions, I need to clarify the given points from the graph. Based on your input:
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Y-Intercept: This is the point where the line intersects the y-axis. From the information provided, you mention points on the y-axis being at -2, 1, and 2. If the line intersects the y-axis at y = 2, then the y-intercept is (0, 2).
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Slope (m): The slope is calculated as the rise over run between two points on the line. If we take two points from your description, for example, (0, 2) (the y-intercept) and (-4, -2), we can find the slope using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using points (0, 2) and (-4, -2): \[ m = \frac{-2 - 2}{-4 - 0} = \frac{-4}{-4} = 1 \] Thus, the slope is 1.
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Equation of the Line in Slope-Intercept Form: The slope-intercept form of a line is given by the equation: \[ y = mx + b \] Where \(m\) is the slope and \(b\) is the y-intercept. Here, with \(m = 1\) and \(b = 2\), the equation is: \[ y = 1x + 2 \quad \text{or simply} \quad y = x + 2 \]
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Type of Relationship: From the information provided, since the slope is positive, this indicates that there is a direct (positive) linear relationship between the x and y variables.
To summarize:
- Y-Intercept: (0, 2)
- Slope: 1
- Equation of the Line: \(y = x + 2\)
- Type of Relationship: Positive linear relationship.
3 answers