Answer: y
=
−
2
3
x
+
2
Explanation:
Given that we have the slope and a point on the graph we can use the point slope formula to find the equation of the line.
Point-Slope Formula:
y
−
y
1
=
m
(
x
−
x
1
)
, where
m
is the slope of the line and
x
1
and
y
1
are x and y coordinates of a given point.
We can summarize the information already given:
m
=
−
2
3
x
1
=
6
y
1
=
−
2
Using this information, we can substitute these values onto the point-slope formula:
y
−
(
−
2
)
=
−
2
3
(
x
−
(
6
)
)
y
+
2
=
−
2
3
(
x
−
6
)
The equation above is the equation of the line in point-slope form. If we wanted to have the equation in
y
=
m
x
+
b
form then we simply solve the equation above for
y
y
+
2
=
−
2
3
x
+
12
3
y
+
2
−
2
=
−
2
3
x
+
12
3
−
2
y
=
−
2
3
x
+
12
3
−
2
(
3
3
)
y
=
−
2
3
x
+
12
3
−
6
3
y
=
−
2
3
x
+
6
3
y
=
−
2
3
x
+
2y
=
−
2
3
x
+
2
Explanation:
Given that we have the slope and a point on the graph we can use the point slope formula to find the equation of the line.
Point-Slope Formula:
y
−
y
1
=
m
(
x
−
x
1
)
, where
m
is the slope of the line and
x
1
and
y
1
are x and y coordinates of a given point.
We can summarize the information already given:
m
=
−
2
3
x
1
=
6
y
1
=
−
2
Using this information, we can substitute these values onto the point-slope formula:
y
−
(
−
2
)
=
−
2
3
(
x
−
(
6
)
)
y
+
2
=
−
2
3
(
x
−
6
)
The equation above is the equation of the line in point-slope form. If we wanted to have the equation in
y
=
m
x
+
b
form then we simply solve the equation above for
y
y
+
2
=
−
2
3
x
+
12
3
y
+
2
−
2
=
−
2
3
x
+
12
3
−
2
y
=
−
2
3
x
+
12
3
−
2
(
3
3
)
y
=
−
2
3
x
+
12
3
−
6
3
y
=
−
2
3
x
+
6
3
y
=
−
2
3
x
+
2
Explanation: