day 4

Day 4

The objective of day 4 is to teach students how to graph linear inequalities. 

If we recall how to solve this, we would solve for x

Then we would see that x is greater than -5, which means we would draw an  circle around -5 shade everything to the right of -5.

The progressions for solving two variable linear inequalities are very similar. 

(1) Graph the region of the linear inequality

Looking at yhr inequality, we should notice a a lot things. It is in Slope-Intercept form (y = mx+b), which means we can identify the slope and y-intercept of this inequality. We will do the inequality sign once we have graphed the picture. We will treat it as an equal sign.

 Let's construct the graph. We can do  a number of ways, either by putting in x values and getting their y values, or we could use the slope and y intercept in the inequality. Let's plot the y intercept and use the slope to form the line. we can see that b = 3, so the y intercept will be (0,3). The slope is m = -2, so we can go down 2 and right 1 (-2/1) or up 2 and left 1 (2/-1) to find the point on the line.

We can  solve for these points on the line algebraically using the slop formula.

We know a point on the line  and the slope, so we can solve for another point.

 Now we have the point (-1,5). Let's find the other one.

We have another point (1,1). We can see these are the points we graphed on the line. We have found them  geometrically.

We can look at the inequality sign. We notice that we have a less than or equal sign.

Let's  think about the equal to part of the inequality. When graphing inequalities in 1 variable, we would draw a circle around the value and shade in the circle because it is in the inequality. With problems in two variables, we don't have a point - we have a linear. We would treat the line in a similar way, by bolding the line to tell that every point on the line is included in the inequality. In other words, every x and y value on the line will make the inequality  true.

Now we have to think about the less than part of the inequality. For inequalities of one problem, we would shade a line.  We will need to shade a region on a side of the line.  If we wanted to shade a region less than the line, we would shade the region to the left, or beneath the line. The part beneath the line will be less than and the part above the line will be greater than. Let's shade the region below the curve.

To assure the correct region, we can pick any point in the region, put it into the inequality and see if the problem is true. We can see that the region has the origin, so let's plug in the point (0,0).

Quiz

1)3x+5y<15

A)Dashed line with negative slope shaded below on the left.

B)Solid line with negative slope shaded below on the left.

C)Dashed line with a positive slope on shaded below on the right. 

2)4y> 3x + 24

A)Dashed line with positive slope shaded above on the right

B)Solid line with negative slope shaded above and on the right. 

C)Solid line with negative slope shaded above and on the left

3)10x> 5y-15

A)Solid line with negative slope shaded below and on the left

B)Solid line with positive slope shaded below and on the right

C)Solid line with positive slope shaded above and on the left 

Answer Key

1)A

2)B

3)B