Solve the system of inequalities by graphing.
y ≤ 2
y > 4x – 3
Select a line to change it between solid and dotted. Select a region to shade it.
Solve the system of inequalities by graphing. y ≤ 2 y > 4x – 3 Select a line to change it between solid and dotted. Select a region to shade it.
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To solve the system of inequalities by graphing, we will follow these steps:
1. Graph the first inequality, (y leq 2):
– This line is horizontal and crosses the y-axis at 2.
– Since the inequality is “less than or equal to,” use a solid line to indicate that points on the line are included.
– Shade the region below the line (y-values that are less than 2).
2. Graph the second inequality, (y > 4x – 3):
– First, convert it to the equation of the line: (y = 4x – 3).
– Find the y-intercept (0, -3) and the slope (4, which means for every 1 unit you move right, move up 4 units).
– Plot the points to draw the line.
– Since the inequality is “greater than,” use a dotted line to indicate that points on the line are not included.
– Shade the region above the line (y-values that are greater than (4x – 3)).
3. Identify the solution set:
– The solution to the system of inequalities is the region where the shaded areas of both inequalities overlap.
4. Final note:
– You should have one solid line at (y = 2) and one dotted line for (y = 4x –