Find the coordinates of three more points that lie on the line passing through the points (0, 0) and (3, -4). Explain your method.

All you need to know here is that the slope of the line contains a set of directions that allow you to start from a point that lies on a given line and find other points that lie on the same line.

So, you know that a given line has a slope of

m

=

1

2

As you know, the slope of a line is defined as the change in  

y

, or  

Δ

y

, divided by the change in  

x

, or  

Δ

x

m

=

Δ

y

Δ

x

Now, you know that the point  

(

7

,

−

2

)

lies on this line. The change in  

y

tells you the number of positions that you must move up on the  

y

axis in order to find the  

y

-coordinate of another point that lies on the line.

Similarly, the change in  

x

tells you the number of positions that you must move to the right on the  

x

axis in order to find the  

x

coordinate of another point that lies on the line.

In this case, you have

m

=

1

2

⇒

{

Δ

y

=

1

Δ

x

=

2

So, if you start at  

x

=

7

, you must move  

2

positions to the right to find

x

2

=

7

+

2

=

9

Similarly, if you start at  

y

=

−

2

, you mus move  

1

position up to find

y

2

=

−

2

+

1

=

−

1

Therefore, a second point on the given line is  

(

9

,

−

1

)

.

Now here comes the cool part, You can use multiples of the slope to find additional points by starting from the same point  

(

7

,

−

2

)

. For example, you have

m

=

1

2

=

2

4

This means that you will get

{

x

3

=

7

+

4

=

11

y

3

=

−

2

+

2

=

0

⇒

(

11

,

0

)

is another point that lies on the line

Similarly, you can also have

m

=

1

2

=

−

1

−

2

In this case, you're moving  

2

positions to the left for  

x

and  

1

position down for  

y

.

This means that

{

x

4

=

7

+

(

−

2

)

=

5

y

4

=

−

2

+

(

−

1

)

=

−

3

⇒

(

5

,

−

3

)

is another point that lies on the line

Therefore, you can say that  

(

5

,

−

3

)

,  

(

7

,

−

2

)

,  

(

9

,

−

1

)

, and  

(

11

,

0

)

are all points that lie on the given line.

To double-check the result, use one of the points to write the equation of the line

(

y

−

y

4

)

=

m

⋅

(

x

−

x

4

)

y

−

0

=

1

2

⋅

(

x

−

11

)

y

=

1

2

x

−

11

2

The line looks like this

graph{1/2x - 11/2 [-10, 10, -5, 5]}

As you can see, all the points that we've found lie on the li

Step-by-step explanation:

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.

18.8cm hope i at all

step-by-step explanation: