Graph the first-degree inequality in two unknowns.
y > 4x -4
Thank you very much. I am not sure what a > is
As you know,
y = 4x-4
is just a line. All the points on the line satisfy the equation.
> means "greater than". So, if (2,4) is on the line, (2,5),(2,6),... are above the line, where y > 4x-4.
So, the solution to an inequality is a whole region of the plane, not just a line. See the graph at
http://www.wolframalpha.com/input/?i=y+%3E+4x-4
To graph the first-degree inequality y > 4x - 4, you'll need to follow these steps:
1. Start by graphing the equation y = 4x - 4. Treat it as if it were an equation by replacing the inequality symbol with an equal sign.
- First, find two points on the line. One way to do this is to choose arbitrary values for x and calculate the corresponding y values.
- Let's choose x = 0. When x = 0, y = 4(0) - 4 = -4.
- Let's choose x = 2. When x = 2, y = 4(2) - 4 = 4.
- So, with the points (0, -4) and (2, 4), you can plot a line passing through these two points on the coordinate plane.
2. To determine which region to shade, you need to understand the meaning of the inequality symbol >. It translates to "greater than" and indicates that the shaded region is above the line y = 4x - 4.
3. Choose a point that is not on the line (0,0) is a commonly used point. Substitute the x and y values of the point into the inequality and check if the inequality holds true or false.
- Let's substitute x = 0 and y = 0:
- 0 > 4(0) - 4
- 0 > -4
- Since the inequality is false, the shaded region does not include the point (0, 0).
4. Finally, shade the region above the line, excluding the line itself. This shaded region represents the solutions to the inequality y > 4x - 4.
Remember, for first-degree inequalities, a dashed line indicates exclusion, and shading indicates the region of solutions.