Answer to Question #103824 in Algebra for tyler

Question

Graph the following and then answer the questions given below: 2x-3y Greater than or equal to 6

a) Describe the method you used to graph this inequality.

b) Where does the line cross the x-axis(write as an ordered pair)?

c) Where does the line cross the y-axis(write as an ordered pair)?

d) Is the origin on the right side or the left side of the line?

e) Is the line solid or dashed?

f) Which side of the line is shaded (left side or right side)?

g) How did you determine which side of the line to shade?

Answer 1

a) The procedure to draw the straight line $2x-3y\ge6$ .

We draw the straight line

$2x-3y =6$ ....(1)

by reducing it into $y=mx+c$

Equation (1) can be written as $3y=2x-6$

Dividing with '3' we get

$$y= \frac{2}{3}x-2$$

$\Rightarrow$ slope $m= \frac{2}{3}$

and y intercept $c= -2$

Since slope $m= \frac{rise}{run}$ , for a rise by 2 units, run will be 3

$\Rightarrow$ $(3,0)$ is a point on the straight line.

Since y intercept $c=-2$ , $(0,-2)$ is a point on the straight line.

Joining these two points and extending it we get a straight line $2x-3y=6$ .

Since $2x-3y\ge6$ is satisfied by the points $x\ge3$ and $y\le-2$

The equation is the points satisfying $x\ge3$ and $y\le-2.$

c) Substituting $x=0$ in the straight line we get $2(0)-3y=6$

$\Rightarrow y=-2$

$(0,-2)$ is a point of intersection with y axis.

b) The point of intersection with $x$ axis is given by substituting $y=0$ in the straight line.

$\Rightarrow 2x-3(0)=6$

$\Rightarrow$ $x=3$

$\Rightarrow$ $(3,0)$ is the point of intersection with $x$ axis.

Therefore, the points of intersection with axes are $(3,0)$ and $(0,-2).$

d) Since the straight line cuts the x axis at $x=3$ and y axis at $y=-2$ and $2x-3y\ge6$ , the origin $(0,0)$ lies to the left of the straight line.

e) Since the straight line includes "equality", the points satisfying $2x-3y=6$ are also to be graphed.

Hence it is a solid line.

f) Right side of the line to be shaded.

g) Since $2x-3y\ge6$ satisfied by $x\ge3$ and $y\le-2$ .