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<[tex]\frac{3}{4} (6) - 3[/tex]
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 [tex]y= [/tex][tex]\frac{3}{4} x-3[/tex] and plotting the point (6,4) and hence you will notice that the point is above the line
Answer:
Step-by-step explanation:
[tex]y<\dfrac{3}{4}x-3\\\\\text{Put the coordinates of the point and check the inequality:}\\\\(6,\ 4)\to x=6,\ y=4\\\\4<\dfrac{3}{4}\cdot6-3\\\\4<\dfrac{18}{4}-3\\\\4<4.5-3\\\\4<1.5\qquad\bold{FALSE}\\\\\text{Therefore your answer is NO, because (6, 4) is above the line.}[/tex]
[tex]\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.}[/tex]
