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\( \square \square \) 4) Given \( f(x)=-\frac{1}{3} x+10 \). The slope is multiplied by 6 and the \( y \)-intercept divided by -5 Describe the changes to parameters \( m \) and \( b \) : The \( y \)-intercept shifts down by 12 . The slope gets steeper. The slope gets less steep. The \( y \)-intercept shifts up by 8 .

Ask by Garrett Wood. in the United States
Feb 03,2025

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The \( y \)-intercept shifts down by 12, and the slope gets steeper.

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When the slope \( m \) of the function \( f(x) = -\frac{1}{3}x + 10 \) is multiplied by 6, it transforms into \( m = -2 \) (since \( -\frac{1}{3} \times 6 = -2 \)). This change indicates that the line becomes steeper, as the absolute value of the slope has increased from \( \frac{1}{3} \) to \( 2 \). For the \( y \)-intercept \( b \), originally 10, if you divide this by -5, it becomes \( b = -2 \) (since \( 10 \div -5 = -2 \)). This indicates that the \( y \)-intercept shifts down by 12 units, jumping from 10 to -2 on the graph. So, both the slope steepens and the point where the line crosses the \( y \)-axis drops significantly!

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