Question

Determine if the ordered pair (6, 4) is a solution to the inequality

Answer 1

Answer:

A

Step-by-step explanation:

all we need to do is to plug the point (6,4) in the inequality and see if it satisfies it :

pay attention that here we have x=6  y=4

4<$\frac{3}{4} (6) - 3$

we simplify we get :

4<4.5-3  

4<1.5  which is incorrect  so (6,4) is not a solution. moreover

notice that 4 is > than 1.5  so the point lies above the line

thus the answer is : A

you can also solve this problem by graphing the line $y=$$\frac{3}{4} x-3$  and plotting the point (6,4)  and hence you will notice that the point is above the line

Answer 2

Answer:

A. No, because (6, 4) is above the line

Step-by-step explanation:

$y$

$\text{Other mathod:}\\\\\text{Show this inequality in the coordinate system.}\\\\\text{Draw the dotted line}\ y=\dfrac{3}{4}x-3.\\\\for\ x=0\to y=\dfrac{3}{4}(0)-3=0-3=-3\to(0,\ -3)\\\\for\ x=4\to y=\dfrac{3}{4}(4)-3=3-3=0\to(4,\ 0)\\\\\text{shaded region below the line}\\\\\text{Mark point (6, 4) and check if it lies in the shaded region.}$