Use simultaneous equations to solve:-
A straight line passes through the points (2, 4) and (-1,-5).
Find its equation.
Answers
Answer:
Step-by-step explanation:
The definition of the slope, m, of the line between two points,
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
is:
m
=
y
2
−
y
2
x
2
−
x
1
Using the given points to compute m:
m
=
−
2
−
5
4
−
−
1
=
−
7
5
The slope-intercept form of the equation of a line is:
y
=
m
x
+
b
Using the slope and the point
(
−
1
,
5
)
, allows us to substitute -1 for x, 5 for y, and
−
7
5
for m, so that we may find the value of b:
5
=
−
7
5
(
−
1
)
+
b
5
=
7
5
+
b
5
−
7
5
=
b
25
5
−
7
5
=
b
b = 18/5
The slope-intercept form of the line that goes through the two given points is:
y
=
−
7
5
x
+
18
5
But we want the form,
a
x
+
b
y
+
c
=
0
, multiply boths side by 5:
5
y
=
−
7
x
+
18
Add
7
x
−
18
to both sides:
7
x
+
5
y
−
18
=
0
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