is this linear equation?
Answers
Answer:
Yes it is a linear equation
y = 10 - 5x =5x
Let us first consider the equality i.e.
5
x
+
y
=
10
or
y
=
10
−
5
x
Now, just pick values for
x
and solve for
y
Let us pick
x
=
0
,
2
and
4
As
y
=
10
−
5
x
,
y
=
10
,
0
and
−
10
and joining points
(
0
,
10
)
,
(
2
,
0
)
and
(
4
,
−
10
)
we get following graph.
graph{10-5x [-20, 20, -10, 10]}
But this is still not the graph for
5
x
+
y
>
10
Observe that this line divides Cartesian plane in three parts.
Part 1 is the line itself and we know on the line
5
x
+
y
=
10
and hence line is not the solution.
Part 2 is the left hand side of the line. One point on the left is
(
0
,
0
)
and if we put these values of
x
and
y
we get
0
, which is less than
10
. Hence in Part 2, we have
5
x
+
y
<
10
. This too is not a solution as what we need is
5
x
+
y
>
10
.
Part 3 is the right hand side of the line. One point to the right is
(
5
,
0
)
and if we put these values of
x
and
y
we get
25
, which is greater than than
10
. Hence in Part 2, we have
5
x
+
y
>
10
and this is the solution and it looks like
graph{5x+y>10 [-20, 20, -10, 10]}
Observe that line is dashed , which shows that points on the line do not form the solution