Answer:
g
=
7
Explanation:
Single value slope (gradient) fixes the curve as a straight line. So we are talking about the standard equation form
y
=
m
x
+
c
where
m
is the gradient.
Gradient
→
m
=
−
5
=
change in y-axis
change in x-axis
Let point 1 be
P
1
→
(
x
1
,
y
1
)
=
(
−
4
,
−
8
)
Let point 2 be
P
2
→
(
x
2
,
y
2
)
=
(
−
7
,
g
)
−
5
=
change in y-axis
change in x-axis
=
−
8
−
g
−
4
−
(
−
7
)
−
5
=
−
8
−
g
3
multiply both sides by 3
−
5
×
3
=
(
−
8
−
g
)
×
3
3
But
−
5
×
3
=
−
15
and
3
3
=
1
−
15
=
−
8
−
g
←
corrected 15 to -15
Add 8 to both sides
−
7
=
−
g
Multiply both sides by (-1)
7
=
+
g
g
=
7
