Graph the following linear inequalities.
1. y 5x + 2
2. y 4x + 2
3. y 3x + 2
4. y 2x + 2
5. y 3x + - 2
6. y 5x - 3
1. y 5x + 2
2. y 4x + 2
3. y 3x + 2
4. y 2x + 2
5. y 3x + - 2
6. y 5x - 3
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Well it's been more than 15 minutes but here are the answers.
These are all equations for lines. They are in slope-intercept form, which is
y = mx + b
where m represents the slope and b represents the y-intercept. Remember, if the slope is positive the line is leaning to the right, and if its negative the line is leaning to the left.
The inequality signs just represent specific regions.
1.) y > 5x + 2
So graph y = 5x + 2, which is a straight line that intersects the y-axis at 2 and has a slope of 5/1. Because this is a strict inequality, >, make the line a dashed line. This represents that the line is not included. Now, the inequality states that y > 5x + 2, meaning y is greater than. So you shade in the region to the left of this line because that is the part that includes the positive values of y. Do you get it? If Y is greater than the equation, the solution region has to include numbers that make y positive and increasing.
2.) y
So you graph a line with a slope of 4/1 that intersects the y-axis at 2. This time, we need y to be less than or equal to, so don't make a dashed line, make a solid line. Now, you shade in the area to the right because this includes the region with the negative y-values.
3.) y
The line has a slope of 3/1 and the y-intercept is 2. Again, make a solid line and shade in the region to the left. Remember, the shaded region will be positive if the sign is > and the shaded region will include the negative y values if the sign is <. It's quite simple.
4.) y
So the line has a slope of 2/1 and the y-intercept is again 2. Because it's less than OR EQUAL TO, once more you make a solid line and shade in the region to the left because we need the negative y values.
5.) y
This means the y-intercept is - 2 and the line has a slope of 3. Again we shade in the left lower region with a solid line.
6.) y > 5x - 3
This time we have a > sign with no equal to, so we make a dashed line. The line intersects the y-axis at -3 and has a slope of 5/1. We shade the upper right region for the positive y-values.
These are all equations for lines. They are in slope-intercept form, which is
y = mx + b
where m represents the slope and b represents the y-intercept. Remember, if the slope is positive the line is leaning to the right, and if its negative the line is leaning to the left.
The inequality signs just represent specific regions.
1.) y > 5x + 2
So graph y = 5x + 2, which is a straight line that intersects the y-axis at 2 and has a slope of 5/1. Because this is a strict inequality, >, make the line a dashed line. This represents that the line is not included. Now, the inequality states that y > 5x + 2, meaning y is greater than. So you shade in the region to the left of this line because that is the part that includes the positive values of y. Do you get it? If Y is greater than the equation, the solution region has to include numbers that make y positive and increasing.
2.) y
So you graph a line with a slope of 4/1 that intersects the y-axis at 2. This time, we need y to be less than or equal to, so don't make a dashed line, make a solid line. Now, you shade in the area to the right because this includes the region with the negative y-values.
3.) y
The line has a slope of 3/1 and the y-intercept is 2. Again, make a solid line and shade in the region to the left. Remember, the shaded region will be positive if the sign is > and the shaded region will include the negative y values if the sign is <. It's quite simple.
4.) y
So the line has a slope of 2/1 and the y-intercept is again 2. Because it's less than OR EQUAL TO, once more you make a solid line and shade in the region to the left because we need the negative y values.
5.) y
This means the y-intercept is - 2 and the line has a slope of 3. Again we shade in the left lower region with a solid line.
6.) y > 5x - 3
This time we have a > sign with no equal to, so we make a dashed line. The line intersects the y-axis at -3 and has a slope of 5/1. We shade the upper right region for the positive y-values.
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Jerk. JediMaster did well explaining it.
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