Question

Which are points on the graph of y = 1.5+ [x]? Select three options

Answer 1

Answer:

The point (4.5 , 6) lies on the graph

Step-by-step explanation:

* Lets explain how to prove that a point lies on a graph

- Substitute x and y by the coordinates of the point, if the

 left hand side (L.H.S) equals the right hand side (R.H.S) then the

 point lies on the graph OR

- Substitute x by the x-coordinate of the point to find y if the the

 value of y equals the y-coordinate of the point, then the point lies

 on the graph OR

- Substitute y by the y-coordinate of the point to find x if the the

 value of x equals the x-coordinate of the point, then the point lies

 on the graph

* Lets solve the problem

∵ The equation is y = 1.5 + 5

# Point (-4.5 , -2.5)

∵ x = -4.5 and y = -2.5

∴ -2.5 = 1.5 + (-4.5)

- Remember (+)(-) = (-)

∴ -2.5 = 1.5 - 4.5

∴ -2.5 = -3

∵ L.H.S ≠ R.H.S

∴ The point (-4.5 , -2.5) does not lie on the graph

# Point (-0.8 , 0.5)

∵ x = -0.8 and y = 0.5

∴ 0.5 = 1.5 + (-0.8)

∴ 0.5 = 1.5 - 0.8

∴ 0.5 = 0.7

∵ L.H.S ≠ R.H.S

∴ The point (-0.8 , 0.5) does not lie on the graph

# Point (7.9 , 9.5)

∵ x = 7.9 and y = 9.5

∴ 9.5 = 1.5 + 7.9

∴ 9.5 = 9.4

∵ L.H.S ≠ R.H.S

∴ The point (7.9 , 9.5) does not lie on the graph

# Point (4.5 , 6)

∵ x = 4.5 and y = 6

∴ 6 = 1.5 + 4.5

∴ 6 = 6

∵ L.H.S = R.H.S

∴ The point (4.5 , 6) lies on the graph

OR

∵ x = 4.5

∴ y = 1.5 + 4.5

∴ y = 6 ⇒ same value of the y-coordinate of the point

∴ The point (4.5 , 6) lies on the graph

OR

∵ y = 6

∴ 6 = 1.5 + x

- Subtract 1.5 from both sides

∴ 4.5 = x ⇒ same value of the x-coordinate of the point

∴ The point (4.5 , 6) lies on the graph

# Point (1.3 , 3.5)

∵ x = 1.3 and y = 3.5

∴ 3.5 = 1.5 + 1.3

∴ 3.5 = 2.8

∵ L.H.S ≠ R.H.S

∴ The point (1.3 , 3.5) does not lie on the graph

Answer 2

Answer:  The required point that lie on the graph of the given function is

(B) (-0.8, 0.5).

Step-by-step explanation:  We are given to select the points that lie on the graph of the following function :

$y=1.5+[x]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We know that

$[x]=n,~\textup{where n is an integer less than or equal to x}.$

We have

If x = -4.5, then we get

$y=1.5+[-4.5]=1.5+(-5)=-3.5\neq -2.5.$

So, the point (-4.5, -2.5) does not lie on the graph of (i).

If x = -0.8, then we get

$y=1.5+[-0.8]=1.5+(-1)=0.5.$

So, the point (-0.8, 0.5) lie on the graph of (i)

If x = 7.9, then we get

$y=1.5+[7.9]=1.5+7=8.5\neq 9.5.$

So, the point (7.9, 9.5) does not lie on the graph of (i).

If x = 4.5, then we get

$y=1.5+[4.5]=1.5+4=5.5\neq 6.$

So, the point (4.5, 6) does not lie on the graph of (i).

If x = 1.3, then we get

$y=1.5+[1.3]=1.5+1=2.5\neq 3.5.$

So, the point (1.3, 3.5) does not lie on the graph of (i).

Thus, the required point that lie on the graph of the given function is

(B) (-0.8, 0.5).