To graph the linear inequality y < 4x - 3, we can start by graphing the corresponding equation, y = 4x - 3.
First, plot the y-intercept, which is -3. The point is (0, -3).
Next, determine the slope, which is 4. The slope represents the ratio of vertical change (rise) to horizontal change (run). For every 4 units of horizontal change, we have 1 unit of vertical change.
Using the slope, plot another point along the line. Start with the y-intercept (0, -3) and move 4 units to the right (horizontal change) and 1 unit up (vertical change). This gives us the point (4, 1).
Draw a straight line connecting these two points. This line represents y = 4x - 3.
Now, to graph the inequality y < 4x - 3, we need to determine if points below or above the line satisfy the inequality. To do this, we can pick a test point that is not on the line.
For simplicity, we can use the origin (0, 0) as the test point. Substitute these coordinates into the inequality:
0 < 4(0) - 3
0 < -3
Since 0 is not less than -3, the point (0, 0) is not part of the solution set. Therefore, the region below the line does not satisfy the inequality.
To shade the region that satisfies the inequality, we need to shade the area above the line. This is done by shading the entire region above the line y = 4x - 3.
The graph of y < 4x - 3 is shown as a dashed line with shading above the line. The shading indicates that any point in the shaded region (above the line) will satisfy the inequality.
Here is a visual representation of the graph described:
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Graph the linear inequality.
y < 4x - 3
1 answer