The difference quotient is
Expand the numerator and you'll see cancellation of a factor of 
(assuming 
):
About 27 miles. It's 26.666666667
Substitute the x-value and see if you get the corresponding y-value. The corresponding y-value an x-value of 3 in this equation should be
Since the coordinate (3,32) does not represent that, it is a false solution
Answer:Step 1) Find the slope.
Step 2) Using the slope, one of the points and the point-slope formula determine the equation.
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.
Substituting the points we are given in this problem the slope is:
m
=
−
10
−
8
2
−
6
m
=
−
18
−
4
m
=
−
2
×
9
−
2
×
2
m
=
−
2
−
2
×
9
2
m
=
1
×
9
2
m
=
9
2
Now we can use one of the points we were given, the slope we determined and the point-slope formula to find the 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.
y
−
8
=
9
2
(
x
−
6
)
If we want to put this into slope-intercept form we can solve for
y
:
y
−
8
=
9
2
x
−
(
9
2
×
6
)
y
−
8
=
9
2
x
−
(
9
×
3
)
y
−
8
=
9
2
x
−
27
y
−
8
+
8
=
9
2
x
−
27
+
8
y
−
0
=
9
2
x
−
19
y
=
9
2
x
−
19
Step-by-step explanation:
