To find the slope of the line that goes through the points (0, 8), (10, 4), and (20, 0), we can use the formula for the slope \( m = \frac{Y_2 - Y_1}{X_2 - X_1} \).
Let's calculate the slope between the first two points (0, 8) and (10, 4):
- \( X_1 = 0 \), \( Y_1 = 8 \)
- \( X_2 = 10 \), \( Y_2 = 4 \)
Calculating the slope:
\[ m = \frac{4 - 8}{10 - 0} = \frac{-4}{10} = -\frac{2}{5} = -0.4 \]
Next, we can also confirm the slope between the second two points (10, 4) and (20, 0):
- \( X_1 = 10 \), \( Y_1 = 4 \)
- \( X_2 = 20 \), \( Y_2 = 0 \)
Calculating the slope:
\[ m = \frac{0 - 4}{20 - 10} = \frac{-4}{10} = -\frac{2}{5} = -0.4 \]
So, the slope is consistent at -0.4.
Filling in the blanks for slope:
The slope \( m \) can be expressed as \( -4/10 \) (which is equivalent to -0.4) or \( -10/4 \) (which is not equivalent to -0.4). However, -10/4 simplifies to -2.5, which is incorrect, meaning only -4/10 gives us -0.4.
For blank 1 - a correct option is:
- G: -4/10.
For blank 2 - using the decimal values for the slope, we will pick:
- H: -0.4.
Determining the y-intercept
From the coordinate (0, 8), we see the y-intercept is directly where the line meets the y-axis. Thus, the y-intercept is:
C: 8.
Equation of the line
Using the slope \( m = -0.4 \) and y-intercept \( b = 8 \), the equation of the line in slope-intercept form \( y = mx + b \) is:
\[ y = -0.4x + 8. \]
Summary of Answers:
- For blank 1: G (-4/10)
- For blank 2: H (-0.4)
- Y-intercept: C (8)
- Equation of the line: \( y = -0.4x + 8 \).
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