graph 4x-3y>=-12
graph -x+5y>=1
for the first one, see
www.wolframalpha.com/input/?i=4x-3y%3E%3D-12
there are lots of online graphing sites you can use for this kind of stuff
Go on:
wolframalpha.c o m
When page be open in rectangle type:
plot 4x-3y>=-12
and click option =
In rectangle type:
plot 4x-3y>=-12
and click option =
My typo:
plot 4x-3y>=-12
and click option =
In rectangle type:
plot -x+5y>=1
and click option =
To graph the inequalities 4x - 3y ≥ -12 and -x + 5y ≥ 1, we will plot the corresponding equations first and then shade the region that satisfies the inequalities.
To plot the equation 4x - 3y = -12, we can rearrange it in the slope-intercept form (y = mx + b):
-3y = -4x - 12
Dividing both sides by -3, we get:
y = (4/3)x + 4
To plot the equation -x + 5y = 1, we can rearrange it in the slope-intercept form:
5y = x + 1
Dividing both sides by 5, we get:
y = (1/5)x + (1/5)
Now, let's graph these two equations on the same coordinate system:
1. Choose a range for the x-axis and y-axis. Let's say -10 to 10 for both axes.
2. Plot the equation y = (4/3)x + 4:
- Start by plotting the y-intercept at (0, 4).
- Use the slope (4/3) to find additional points.
- For example, move 3 units to the right from the y-intercept (0,4), which gives you the point (3,8).
- Connect the points to form a line.
3. Plot the equation y = (1/5)x + (1/5):
- Start by plotting the y-intercept at (0, 1/5).
- Use the slope (1/5) to find additional points.
- For example, move 5 units to the right from the y-intercept (0,1/5), which gives you the point (5,2).
- Connect the points to form a line.
Now, let's shade the region that satisfies the inequalities:
- For the inequality 4x - 3y ≥ -12:
- Choose any point not on the line (e.g., the origin at (0,0)).
- Substitute the x and y values into the inequality.
- If the inequality is true, shade the region that contains the point. Otherwise, shade the opposite region.
- For example, substituting (0,0) into the inequality gives: 4(0) - 3(0) ≥ -12, which is true.
- Therefore, shade the region above the line.
- For the inequality -x + 5y ≥ 1:
- Repeat the above steps for this inequality.
- For example, substituting (0,0) into the inequality gives: -(0) + 5(0) ≥ 1, which is not true.
- Therefore, shade the region below the line.
The shaded regions will indicate the solutions to the inequalities, and any point within those shaded regions will satisfy both inequalities simultaneously.