The equation \( y = -2x - 8 \) is a linear equation in slope-intercept form, which is typically written as \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
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Slope (m): The coefficient of \( x \) is \(-2\), which means the slope of the line is \(-2\). This indicates that for every unit increase in \( x \), \( y \) decreases by \( 2 \) units. Therefore, the line is decreasing.
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Y-intercept (b): The constant term is \(-8\), which means the y-intercept occurs at the point \( (0, -8) \) on the coordinate plane. This is the point where the line crosses the y-axis.
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X-intercept: To find the x-intercept, set \( y = 0 \) and solve for \( x \): \[ 0 = -2x - 8 \ 2x = -8 \ x = -4 \] Thus, the x-intercept is at the point \( (-4, 0) \).
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Graph: The line represented by this equation will slope downwards from left to right, starting at the y-intercept of \(-8\) on the y-axis and crossing the x-axis at \(-4\).
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General Behavior: Since the slope is negative, as \( x \) increases, \( y \) becomes smaller (more negative). Thus, this linear function represents a decreasing relationship between \( x \) and \( y \).
Overall, the equation represents a straight line with a negative slope and can be graphed to visualize these properties.