What is the slope of the line with an x-intercept of 4 and a y-intercept of -3?
Answers
Step-by-step explanation:
Consider the standardised form of
y
=
m
x
+
c
Determine the value of
c
The x-axis crosses the y-axis at
x
=
0
So if we substitute 0 for
x
we have:
y
intercept
=
m
(
0
)
+
c
m
×
0
=
0
so we end up with
y
intercept
=
c
but the question give the value of the y-intercept as -5 so we have
c
=
−
5
and the equation now becomes
y
=
m
x
+
c
dddd
→
dddd
y
=
m
x
−
5
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Determine the value of
m
m
is the slope (gradient) which is
change in
y
change in
x
VERY IMPORTANT
When determining the gradient you read left to right on the x-axis
Let the left most point be
P
1
→
(
x
1
,
y
1
)
=
(
0
,
−
5
)
...
(y-intercept)
Let the right most point be
P
2
→
(
x
2
,
y
2
)
=
(
4
,
0
)
...
...
(x-intercept)
m
=
change in
y
change in
x
=
y
2
−
y
1
x
2
−
x
1
=
0
−
(
−
5
)
4
−
0
Note that
−
(
−
5
)
is the same as
+
5
m
=
0
+
5
4
−
0
=
+
5
4
so the equation becomes
y
=
m
x
−
5
dddd
→
dddd
y
=
5
4
x
−
5
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