To find the slope \( M \) that goes through the points, we can use the formula for slope:
\[ M = \frac{Y_2 - Y_1}{X_2 - X_1} \]
Let's take the first two points \((0, 8)\) and \((10, 4)\):
\[ M = \frac{4 - 8}{10 - 0} = \frac{-4}{10} = -\frac{2}{5} = -0.4 \]
Now, we'll also check the slope between the second point \((10, 4)\) and the third point \((20, 0)\):
\[ M = \frac{0 - 4}{20 - 10} = \frac{-4}{10} = -\frac{2}{5} = -0.4 \]
Since both calculations give the same result, the slope \( M \) is consistent.
Slope Choices:
The options given do not include -0.4. Let’s express -0.4 in terms of the options provided:
- -0.4 can be represented as \(-\frac{4}{10}\).
- Checking against the list:
- C: -10/4 (Not equal to -0.4)
- D: -10 (Not equal to -0.4)
- F: -4 (Not equal to -0.4)
- G: -4/10 (Not equal to -0.4, equals -0.4 after simplification)
- Thus, the correct answer for the slope that fits the line is G: -4/10.
Y-Intercept:
The y-intercept occurs when \( X = 0 \). From the given points, at \( X = 0 \), \( Y = 8 \).
Y-Intercept Choices:
According to the choices given:
- C: 8 (Correct)
Equation of the Line:
The equation of the line can be expressed in slope-intercept form \( Y = MX + B \).
Where:
- \( M = -0.4 \) or \( -\frac{2}{5} \)
- \( B = 8 \)
Thus, the equation of the line is:
\[ Y = -0.4X + 8 \]
Summarizing:
- Slope \( M \): -4/10
- Y-intercept \( B \): 8
- Equation of the line: \( Y = -0.4X + 8 \)
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