Q:

Describe the graph of the inequality y > 1/2 x + 4A.) The line is solid and shading is above the line.B.) The line is dashed and shading is below the line.C.) The line is solid and shading is below the line.D.) The line is dashed and shading is above the line

Accepted Solution

A:
Because we are using a greater than symbol(>) in this inequality, rather than a greater than or equal to sign( ≥ ) we will be using the dashed line.

the solid line: tells us that the values lying on the line make the inequality true. On the line the x side of the equation will EQUAL y. 

the dashed line: the x values will still solve the inequality as being qual to y, but the inequality did not ask for equal values. Only values that mak y greater than the other side of the inequality. 

Shading: occurs over the coordinates that make the inequality true. ( in this case above the dashed line.)

For example, 

we know the y-intercept would be (0,4) if this were an equation. 

If you plug in (0,3) which is a point below the line is the equality true or false?
y> 0.5x+4
(3)>0.5(0)+4
3>4
is this true? 
NO. therefore, values below the line are NOT shaded.  

How about values above the line like (0,5)


If you plugged in (0,5) the inequality would be true. Therefore, in this case we shade above the line. 

Answer: D) The line is dashed and shading is above the line

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