To represent the function rule \( y = -2x - 1 \), we can identify key characteristics of the equation, which is in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
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Slope (m): The slope is \(-2\), which means for every unit increase in \( x \), \( y \) decreases by 2 units. This indicates that the graph will be a straight line slanting downwards from left to right.
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Y-intercept (b): The y-intercept is \(-1\), which means the graph crosses the y-axis at the point (0, -1).
To sketch the graph:
- Start at the point (0, -1) on the y-axis.
- From this point, because the slope is \(-2\), you will move right 1 unit (increase \( x \) by 1) and down 2 units (decrease \( y \) by 2) to find another point on the line. This gives you the point (1, -3).
- Repeat this process or use any two points to draw the line that represents the function.
Final Note:
If you have options for graphs to choose from, look for a straight line that:
- Crosses the y-axis at -1.
- Slopes downward to the right (meaning it decreases as \( x \) increases).
If you have specific graphs in front of you, apply these points to identify which one represents the function \( y = -2x - 1 \).