To graph the line given by the equation \( y = 6x + 4 \), you'll want to start with the slope and the y-intercept.
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Identify the y-intercept: The y-intercept occurs when \( x = 0 \). From the equation, when \( x = 0 \): \[ y = 6(0) + 4 = 4 \] So the y-intercept is the point \( (0, 4) \).
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Identify the slope: The slope (m) is 6, which means for every 1 unit you move to the right (increase in \( x \)), you will move 6 units up (increase in \( y \)). Therefore, from the y-intercept (0, 4), you can find another point using the slope:
- Starting from \( (0, 4) \), move 1 unit right to \( (1, 4) \) and then move 6 units up to \( (1, 10) \). So another point on the line is \( (1, 10) \).
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Draw the graph:
- Plot the points \( (0, 4) \) and \( (1, 10) \) on the graph.
- Draw a straight line through these points, extending it in both directions.
You can also find more points using the equation by substituting other values for \( x \):
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If \( x = -1 \), \[ y = 6(-1) + 4 = -6 + 4 = -2 \quad \text{(Point: } (-1, -2) \text{)} \]
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If \( x = 2 \), \[ y = 6(2) + 4 = 12 + 4 = 16 \quad \text{(Point: } (2, 16) \text{)} \]
By plotting multiple points like \( (0, 4) \), \( (1, 10) \), \( (-1, -2) \), and \( (2, 16) \), you can create a more accurate line on your graph.
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