To convert the inequality \( 14x + 7y > 21 \) from standard form to slope-intercept form (which is of the format \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), we need to isolate \( y \).
Let's solve this step by step:
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Start with the original inequality: \[ 14x + 7y > 21 \]
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Subtract \( 14x \) from both sides: \[ 7y > -14x + 21 \]
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To solve for \( y \), divide every term by \( 7 \): \[ y > -2x + 3 \]
Now, the inequality is in slope-intercept form.
From \( y > -2x + 3 \):
- The slope \( m \) is \( -2 \).
- The y-intercept \( b \) is \( 3 \).
Summary: The inequality in slope-intercept form is \( y > -2x + 3 \).
- Slope: \( -2 \)
- Y-intercept: \( 3 \)
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