Bot GPT 4-o mini To identify the slope and y-intercept of the given linear equation \( y = -\frac{1}{4}x + 2 \), we can compare it to the slope-intercept form of a linear equation, which is given by:
\[ y = mx + b \]
where:
- \( m \) is the slope,
- \( b \) is the y-intercept.
From the equation \( y = -\frac{1}{4}x + 2 \):
- The slope \( m = -\frac{1}{4} \).
- The y-intercept \( b = 2 \).
Summary
- Slope (m): \(-\frac{1}{4}\)
- Y-intercept (b): \(2\)
Graphing the Equation
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Plot the y-intercept: Start by plotting the y-intercept on the graph, which is the point (0, 2).
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Use the slope to find another point: The slope of \(-\frac{1}{4}\) indicates that for every 1 unit increase in \( y \), \( x \) increases by 4 units (going downwards because the slope is negative).
- From the point (0, 2): move down 1 unit to (1, 1.75) and move to the right 4 units. This gives you the point (4, 1).
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Draw the line: Use a ruler to draw a straight line through the points (0, 2) and (4, 1).
Graph
Here is a description of the graph layout:
- Draw a vertical axis (y-axis) and a horizontal axis (x-axis).
- Mark the point (0, 2) on the y-axis.
- Mark the point (4, 1).
- Draw a straight line through these two points extending in both directions.
This visual representation serves to illustrate the relationship defined by the linear equation \( y = -\frac{1}{4}x + 2 \).
1 answer