Question

Write an equation in point-slope form of the line that passes through (1,0) and (4,4).

Answer 1

Explanation:
We want this in the form
y
=
m
x
+
c
, where
m
is the gradient, and
c
is the y-intercept.
Gradient is the change in y over the change in x, or the rise over run; however you like to think about it.
m
=
y
2
−
y
1
x
2
−
x
1
So for our points
(
1
,
4
)
and
(
4
,
9
)
m
=
9
−
4
4
−
1
=
5
3
Now, by rearranging our equation for gradient, we can show that:
y
−
y
1
=
m
(
x
−
x
1
)
Here,
x
and
y
are general points on the line - we've just replaced
(
x
2
,
y
2
)
with
(
x
,
y
)
Since we know
m
, and have a set of co-ordinates to sub in as
(
x
1
,
y
1
)
, we can sub values in, then re-arrange to get to the
y
=
m
x
+
c
form.
y
−
4
=
5
3
(
x
−
1
)
y
−
4
=
5
3
x
−
5
3

y
=
5
3
x
−
5
3
+
4

y
=
5
3
x
+
7
3

as required.