the problem is:
4x+y>=4
so after solving for the equation line formula y=mx+b
I got :
y>= -4x+4
the points to plot was:
(-1,8),(0,4),(1,0),(2,-4)
and the line will be solid and the shading for solution would be on top going in that-------> direction.
To understand why the graph of the inequality y >= -4x + 4 is graphed with a solid line and the shading is on top, we need to consider the components of the inequality.
First, let's review the equation we started with: 4x + y >= 4. To graph an inequality, we usually start by converting it into the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
To solve for y in the given inequality, we need to isolate it on one side:
4x + y >= 4
y >= -4x + 4
From this, we can see that the slope of the line is -4 and the y-intercept is 4. With this information, we can begin sketching the graph.
Now let's plot the given points: (-1,8), (0,4), (1,0), and (2,-4). These points lie on the line defined by the inequality.
To draw the line, start by plotting the y-intercept at (0, 4). From this point, use the slope to determine the next points.
Starting from the y-intercept (0, 4), move one unit to the right and four units downward to get the second point (1, 0). Continuing this pattern, move another unit to the right and four units downward to get the third point (2, -4).
To confirm the shape of the line, we can connect these points with a solid line. The solid line is used because the original inequality includes "greater than or equal to" (≥). This means the points on the line are included in the solution.
Finally, let's determine the shading. The inequality y >= -4x + 4 represents all the points that are above the line, including the line itself. Therefore, the solution is shaded above the line, or in the upward direction.
In summary, the graph of the inequality y >= -4x + 4 includes a solid line, which includes the points (-1, 8), (0, 4), (1, 0), and (2, -4). The solution is shaded above the line, indicating all the solutions that satisfy the inequality.