Question

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


`y < (3)/(4)x - 3`


A.No, because (6, 4) is above the line
B.Yes, because (6, 4) is below the line
C.Yes, because (6, 4) is on the line
D.No, because (6, 4) is on the line​

Answer 1

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

Explanation:

`y<(3)/(4)x-3\\\\\text{Put the coordinates of the point and check the inequality:}\\\\(6,\ 4)\to x=6,\ y=4\\\\4<(3)/(4)\cdot6-3\\\\4<(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.}`

`\text{Other mathod:}\\\\\text{Show this inequality in the coordinate system.}\\\\\text{Draw the dotted line}\ y=(3)/(4)x-3.\\\\for\ x=0\to y=(3)/(4)(0)-3=0-3=-3\to(0,\ -3)\\\\for\ x=4\to y=(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.}`

Answer 2

A

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<
`(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=`
`(3)/(4) x-3` and plotting the point (6,4) and hence you will notice that the point is above the line