Write the standard form of the equation where p=5 and theta = 90

First, we must determine the slope of the line. The slope can be found by using the formula:
m
=
y
2
−
y
1
x
2
−
x
1
Where
m
is the slope and (
x
1
,
y
1
) and (
x
2
,
y
2
) are the two points on the line.
Substituting the values from the points in the problem gives:
m
=
−
3
−
5
−
3
−
5
=
−
8
−
8
=
1
Next, we can use the point-slope formula to get an equation for the line. The point-slope formula states:
(
y
−
y
1
)
=
m
(
x
−
x
1
)
Where
m
is the slope and
(
x
1
y
1
)
is a point the line passes through.
Substituting the slope we calculated and the first point from the problem gives:
(
y
−
5
)
=
1
(
x
−
5
)
The standard form of a linear equation is:
A
x
+
B
y
=
C
Where, if at all possible,
A
,
B
, and
C
are integers, and A is non-negative, and, A, B, and C have no common factors other than 1
We can now transform the equation we wrote to standard form as follows:
y
−
5
=
x
−
5
−
x
+
y
−
5
+
5
=
−
x
+
x
−
5
+
5
−
x
+
y
−
0
=
0
−
0
−
x
+
y
=
0
−
1
(
−
x
+
y
)
=
−
1
⋅
0
x
−
y
=
0
1
x
+
−
1
y
=
0