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Answer :
Final answer:
The accurate equation for the graphed function is g(x) = |x-1| + 3. This expression correctly reflects the observed features, including a y-intercept at 3 and an absolute value function.
Explanation:
The correct equation that represents the function graphed on the coordinate plane is g(x) = |x-1| + 3. The given information states that the line has a y-intercept of 9 and a slope of 3. This means that the line intersects the y-axis at the point (0, 9) and for every increase of 1 on the x-axis, the line rises 3 units on the y-axis.
The equation g(x) = |x-1| + 3 represents this relationship. The absolute value function |x-1| ensures that the line will always have a positive slope and the +3 term accounts for the y-intercept.
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