To compare the slopes and intercepts of the functions \( f(x) \) (which you mentioned is shown in a graph) and \( g(x) = -6x + 3 \), we need to analyze the slope and intercepts of both functions.
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Slope: The slope of a linear function \( y = mx + b \) is given by \( m \).
- For \( g(x) = -6x + 3 \), the slope \( m \) is -6.
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Y-Intercept: The y-intercept is the value of \( b \) in the function \( y = mx + b \).
- For \( g(x) = -6x + 3 \), the y-intercept is 3.
Now, we need to determine the slope and y-intercept of the function \( f(x) \) from its graph. Since I can't view the graph directly, you would need to identify:
- The slope of \( f(x) \) (let's call it \( m_f \)).
- The y-intercept of \( f(x) \) (let's call it \( b_f \)).
Based on the information we have:
- If \( m_f = -6 \) and \( b_f = 3 \), then the answer would be A: "Both the slopes and the y-intercepts are the same."
- If \( m_f \neq -6 \) and \( b_f = 3 \), then the answer would be B: "The slopes are different but the y-intercepts are the same."
- If \( m_f = -6 \) and \( b_f \neq 3 \), then the answer would be C: "The slopes are the same but the intercepts are different."
- If both \( m_f \neq -6 \) and \( b_f \neq 3\), then the answer would be D: "Both the slopes and the y-intercepts are different."
You can determine which option applies by matching the slope and intercept of \( f(x) \) to those of \( g(x) \).
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