To graph the equation \( y = 4x + 5 \), you can follow these steps:
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Identify the y-intercept: The equation is in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Here, the y-intercept \( b \) is 5. This means the graph crosses the y-axis at the point (0, 5).
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Determine the slope: The slope \( m \) is 4. This means that for every 1 unit you move to the right along the x-axis, the value of y increases by 4 units.
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Plot another point using the slope: Starting from the y-intercept (0, 5):
- Move 1 unit to the right (to x = 1) and then move 4 units up (to y = 9). This gives you another point: (1, 9).
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Plot these two points on the graph:
- (0, 5)
- (1, 9)
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Draw the line: Use a ruler to draw a straight line through the two points, extending it in both directions.
Now, you have successfully graphed the equation \( y = 4x + 5 \). The line should slope upwards to the right, indicating a positive relationship between x and y.