Question

Which two points are on the graph of y=-x+ 3?

O (1, 2), (0, -3)
O (0,3), (4, -1)
EN Page
O (-1, -2), (1, 4)
O (4, -1), (1,3)

Answer 1

(0,3), (4, -1)

Explanation:

we have

`y=-x+3`

This is a linear equation (The graph is a line)

we know that

If a ordered pair is on the graph of the line, then the ordered pair must satisfy the equation of the line

Verify each case

case 1) (1, 2), (0, -3)

First point

x=1,y=2

substitute in the equation and then compare the result

`2=-1+3`

`2=2` ---> is true

so

The first point is on the graph

Second point

x=0,y=-3

substitute in the equation and then compare the result

`-3=-0+3`

`-3=3` ---> is not true

so

The second point is not on the graph

therefore

The two points are not on the graph

case 2) (0,3), (4, -1)

First point

x=0,y=3

substitute in the equation and then compare the result

`3=0+3`

`3=3` ---> is true

so

The first point is on the graph

Second point

x=4,y=-1

substitute in the equation and then compare the result

`-1=-4+3`

`-1=-1` ---> is true

so

The second point is on the graph

therefore

The two points are on the graph

case 3) (-1, -2), (1,4)

First point

x=-1,y=-2

substitute in the equation and then compare the result

`-2=-(-1)+3`

`-2=4` ---> is not true

so

The first point is not on the graph

therefore

The two points are not on the graph

case 4) (4, -1), (1,3)

First point

x=4,y=-1

substitute in the equation and then compare the result

`-1=-4+3`

`-1=-1` ---> is true

so

The first point is on the graph

Second point

x=1,y=3

substitute in the equation and then compare the result

`3=-1+3`

`3=2` ---> is not true

so

The second point is not on the graph

therefore

The two points are not on the graph