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To graph the line \( y = -7x - 1 \), plot the y-intercept at \( (0, -1) \), use the slope of -7 to find another point, and draw a straight line through these points.
Solution
To graph the line given by the equation \( y = -7x - 1 \), we can follow these steps:
1. **Identify the slope and y-intercept**:
- The equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
- Here, the slope \( m = -7 \) and the y-intercept \( b = -1 \).
2. **Plot the y-intercept**:
- Start by plotting the point where the line crosses the y-axis. This occurs at \( (0, -1) \).
3. **Use the slope to find another point**:
- The slope of -7 means that for every 1 unit you move to the right (positive direction on the x-axis), you move 7 units down (negative direction on the y-axis).
- From the point \( (0, -1) \), moving 1 unit to the right takes you to \( (1, -1 - 7) = (1, -8) \). Plot this point.
4. **Draw the line**:
- Connect the two points \( (0, -1) \) and \( (1, -8) \) with a straight line. Extend the line in both directions.
5. **Label the axes**:
- Make sure to label the x-axis and y-axis for clarity.
This will give you a visual representation of the line \( y = -7x - 1 \). If you have graphing software or graph paper, you can use these steps to create the graph accurately.
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Simplify this solution Mind Expander
To graph the line \( y = -7x - 1 \), first, identify the slope and the y-intercept from the equation, which tells us that the slope is -7 and the y-intercept is -1. This means the line will slope steeply downwards from left to right. Start by plotting the point (0, -1) on the y-axis, then use the slope to find another point. From (0, -1), move down 7 units and 1 unit to the right to reach the point (1, -8). Connect these points and extend the line! Next, don't forget to label your axes and indicate that it's a linear graph. Lines can show trends in data or relationships in math, making them super useful for visualizing various concepts, from economics to physics!
