To find the rate of change, y-intercept, and the equation of the line in slope-intercept form using the data given in your table, let's first clarify the data points. It seems like there might be a typo or formatting issue in the values you've provided.
Based on typical use, I will interpret your data points as follows:
- Let's assume we have the following points:
- Point 1: (2, 80)
- Point 2: (1, 70)
- Point 3: (0, 40) or another point may be implied (if 405 or 10 corresponds to y-values).
To determine the equation of the line, we can use two points:
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Calculate the slope (rate of change): \[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \]
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For example, let's use (1, 70) as \( (x_1, y_1) \) and (2, 80) as \( (x_2, y_2) \): \[ m = \frac{80 - 70}{2 - 1} = \frac{10}{1} = 10 \]
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Next, find the y-intercept (b) using the equation: \[ y = mx + b \] Using point (1, 70): \[ 70 = 10(1) + b \implies b = 70 - 10 = 60 \]
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The equation of the line in slope-intercept form \( y = mx + b \): \[ y = 10x + 60 \]
Summarizing:
- Rate of change: \( 10 \)
- y-intercept: \( 60 \)
- Equation of the line in slope-intercept form: \( y = 10x + 60 \)
Please clarify or specify any additional data, and I can assist further!