Is this correct.
Graph each of the following inequalities.
4x + y (greater than or equal to) 4
My answer:
y= -4x + 4
Y= mx + b
For b = (0,4)
For x = (-4 , 0)
The line will be a straight line across the positive codent to the negative crodant
In the first case, you have the line location right, but the area where the inequality is valid is also anywhere above the line. You might want to show that area as shaded.
In the second case, I do not understand why they are specifying two values of b and x. You cannot graph the lines unless you know what the slope, m, is. Are those pairs of numbers supposed to be points through which a y = mx + b line passes?
yes
To graph the inequality 4x + y ≥ 4, you can follow these steps:
1. Begin by graphing the line y = -4x + 4 using the slope-intercept form (y = mx + b). The slope (m) is -4, and the y-intercept (b) is 4. Plot the point (0, 4) on the y-axis, and from there, use the slope to find additional points.
2. To find more points on the line, use the slope (m = -4) to determine the change in y and x. For example, since the slope is -4, you can move down 4 units on the y-axis and right 1 unit on the x-axis. Repeat this process to find a few more points.
3. Connect the points using a straight line. Keep in mind that this line represents the equation y = -4x + 4.
4. To determine the shaded area that satisfies the inequality 4x + y ≥ 4, you need to consider the inequality sign. In this case, the inequality is "greater than or equal to," denoted by ≥. Since the line itself is included in the solution, the shaded area should be above or on the line.
5. Shade the area above the line. One way to do this is to shade the area above the line y = -4x + 4. This shaded area represents all the solutions to the inequality.
By following these steps, you can graph the inequality 4x + y ≥ 4 and represent the solution using a shaded region.