I don't understand how to graph y>x+3 or
y<-1/5x-2
Take the first one. Graph
y=x+3 that is the line where y=x+3. But the question is y greater than this, so everything above that line is a solution area.
the question is y is greater or less than -1/5x-2
To graph the inequalities y > x + 3 and y < -1/5x - 2, you can follow these steps:
1. Start by graphing the corresponding equality equations, y = x + 3 and y = -1/5x - 2. These are the boundary lines that separate the solutions from the non-solutions.
For y = x + 3:
- Choose a few values for x and substitute them into the equation to find the corresponding y-values.
- For example, when x = 0, y = 0 + 3 = 3. So one point is (0, 3).
- When x = -3, y = -3 + 3 = 0. So another point is (-3, 0).
- Connect these points to draw a straight line. This is the boundary line for y > x + 3.
For y = -1/5x - 2:
- Again, select some x-values and find the corresponding y-values.
- For example, when x = 0, y = -1/5 * 0 - 2 = -2. So one point is (0, -2).
- When x = -5, y = -1/5 * -5 - 2 = 1. So another point is (-5, 1).
- Connect these points to draw a straight line. This is the boundary line for y < -1/5x - 2.
2. Once you have the boundary lines graphed, you need to determine which side of each boundary line satisfies the given inequality.
For y > x + 3:
- Choose a point not on the line, like the origin (0, 0).
- Substitute the x and y values of the point into the inequality: 0 > 0 + 3.
- Since 0 is not greater than 3, the point (0, 0) does not satisfy the inequality.
- Shade the region above the boundary line to represent the solutions for y > x + 3.
For y < -1/5x - 2:
- Repeat the same process by substituting the x and y values of a point outside the boundary line into the inequality.
- For example, substitute (0, 0) into the inequality: 0 < -1/5 * 0 - 2.
- Since 0 is indeed less than -2, the point (0, 0) satisfies the inequality.
- Shade the region below the boundary line to represent the solutions for y < -1/5x - 2.
3. Finally, the solutions to the system of inequalities are the regions that satisfy all the given inequalities. In this case, the solution will be the shaded region that lies above the line y > x + 3 and below the line y < -1/5x - 2.
Remember to label the boundary lines and shade the appropriate regions to clearly represent the solutions.