To represent the inequality \( y > 3x + 4 \) graphically, follow these steps:
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Graph the boundary line: Start by graphing the equation \( y = 3x + 4 \). This is a straight line with a slope of 3 and a y-intercept of 4.
- The y-intercept is the point (0, 4).
- From (0,4), you can use the slope to find another point. For example, if you move right by 1 unit (to x=1), you move up 3 units (to y=7), giving you the point (1, 7).
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Draw the line: Since the inequality is \( y > 3x + 4 \) (and not \( y \geq 3x + 4 \)), you will draw a dashed line to indicate that points on the line itself are not included in the solution.
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Shade the appropriate region: Since the inequality is \( y > 3x + 4 \), shade the area above the line. This indicates that all points in that region satisfy the inequality.
Make sure when selecting or producing the graph, that it reflects all of these aspects: the dashed line for the boundary and the shaded area above the line.
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