To find the slope of the line through the points in the table, we can use the formula for the slope (m), which is given by:
\[ m = \frac{\text{change in } y}{\text{change in } x} \]
From the points:
- When \( x = 0 \) minutes, \( y = 8 \) miles.
- When \( x = 10 \) minutes, \( y = 4 \) miles.
- When \( x = 20 \) minutes, \( y = 0 \) miles.
Let's calculate the slope between the first two points \( (0, 8) \) and \( (10, 4) \):
\[ m = \frac{4 - 8}{10 - 0} = \frac{-4}{10} = -\frac{2}{5} \]
Next, we can check the slope between the second and third points \( (10, 4) \) and \( (20, 0) \):
\[ m = \frac{0 - 4}{20 - 10} = \frac{-4}{10} = -\frac{2}{5} \]
The slope is consistently \(-\frac{2}{5}\). In decimal form, this equals \(-0.4\), so:
- For blank 1 (the slope), we have: F -4/10
- For blank 2 (the y-intercept), since when \( x = 0 \), \( y = 8\), we have: A 8.
The y-intercept is at \( y = 8 \).
Now, we can write the equation of the line. Using the slope-intercept form \( Y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we have:
\[ Y = -0.4x + 8 \]
Therefore, filling in the blanks:
**Y = F -4/10 × + A 8 **
Final Summary:
- Slope (blank 1): \( -\frac{4}{10} \) (Option F)
- Y-intercept (blank 2): \( 8 \) (Option A)
- Equation of the line: \( Y = -0.4x + 8 \)
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