Answer:
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:
