Newton Hobbs
10/06/2023 · Senior High School
\( \leqslant \quad \) Graph the line \( y=m x+b \) for the given values.
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Tutor-Verified Answer
Step-by-step Solution
To graph the line given by the equation \( y = mx + b \), you need to know the values of the slope \( m \) and the y-intercept \( b \).
1. **Identify the slope \( m \)**: This value indicates how steep the line is. A positive slope means the line rises as it moves from left to right, while a negative slope means it falls.
2. **Identify the y-intercept \( b \)**: This is the point where the line crosses the y-axis. The coordinates of this point are \( (0, b) \).
3. **Plot the y-intercept**: Start by plotting the point \( (0, b) \) on the graph.
4. **Use the slope to find another point**: From the y-intercept, use the slope to find another point on the line. The slope \( m \) can be expressed as a fraction \( \frac{\text{rise}}{\text{run}} \). For example, if \( m = 2 \), you would go up 2 units (rise) and 1 unit to the right (run) to find the next point.
5. **Draw the line**: Once you have at least two points, draw a straight line through them, extending it in both directions.
If you provide specific values for \( m \) and \( b \), I can give you a more detailed step-by-step guide or even a description of the graph!
Quick Answer
To graph \( y = mx + b \), plot the y-intercept \( (0, b) \), use the slope \( m \) to find another point, and draw a line through both points.
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