Directions:Solve and graph equation using words.Then include wether it is solid line or dotted, to graph it,and which side shading is on.
Problem:5x+3y>-6 and 27+x<6
Problem is supposed to be: 5x+3y>-6 and 2y+x<6
put these in order of what you want to plot...
y>-5/3 x-2 draw the dotted line y=-5/3x -2 Notice the equation says y above the dotted line is allowed.
y<-x/2 + 6
draw the dotted line y= - x/2 + 6
Notice the equation says y is less (below) this line
So the allowed area is below the second, and above the first
To solve and graph the equation:
1. Solve the first equation: 5x + 3y > -6
Subtract 5x from both sides: 3y > -5x - 6
Divide both sides by 3: y > -5/3x - 2
This inequality represents a line. To graph it:
a. Start by plotting the y-intercept at -2 on the y-axis.
b. Find another point on the line by using the slope. The slope is -5/3, which means for every 3 units you move horizontally (x-axis), you move 5 units vertically (y-axis).
c. From the y-intercept, move 3 units to the right and 5 units down. Plot this point.
d. Draw a dotted line through the two plotted points. The line should extend infinitely in both directions.
2. Solve the second equation: 2y + x < 6
Subtract x from both sides: 2y < -x + 6
Divide both sides by 2: y < -x/2 + 3
Again, this inequality represents a line. To graph it:
a. Start by plotting the y-intercept at 3 on the y-axis.
b. Find another point on the line using the slope. The slope is -1/2, which means for every 2 units you move horizontally (x-axis), you move 1 unit vertically (y-axis).
c. From the y-intercept, move 2 units to the right and 1 unit down. Plot this point.
d. Draw a dotted line through the two plotted points. The line should extend infinitely in both directions.
Next, determine the shading:
- Since the first inequality is "y > -5/3x - 2," all the points above the line (dotted) are allowed. Shade the region above the line.
- For the second inequality, "y < -x/2 + 3," all the points below the line (dotted) are allowed. Shade the region below the line.
Your graph should show a shaded region below the second line and above the first line.
To solve and graph the equations, follow these steps:
1. Equation 1: 5x + 3y > -6
- Rearrange the equation to isolate y: 3y > -5x - 6
- Divide all terms by 3 to solve for y: y > (-5/3)x - 2
Graph for Equation 1:
- Draw a dotted line with equation y = (-5/3)x - 2.
- Since the equation is greater than, the side above the dotted line is allowed.
- Shade the area above the dotted line.
2. Equation 2: 2y + x < 6
- Rearrange the equation to isolate y: 2y < -x + 6
- Divide all terms by 2 to solve for y: y < (-1/2)x + 3
Graph for Equation 2:
- Draw a dotted line with equation y = (-1/2)x + 3.
- Since the equation is less than, the side below the dotted line is allowed.
- Shade the area below the dotted line.
Finally, the allowed area is the region that is below the second dotted line and above the first dotted line.