The slope is 1/2.
You can figure it out using the rise over run method
First find the x and y values because where the lines will intersect, they share the point of the intersection so they will share the x and y coordinates.
Rearrange equations
To cancel y, we must do equation 1 minus equation 2. Similarly:
So the x coordinate is 3.
The y coordinate can be found with substitution of x into one of the equations:
So where the two lines intersect is at the point (3, 7), which is the solution to the equations.
Divide the coefficient of
x
(not
x
2
) by 2, and then square that.
c
=
144
.
Explanation:
Divide the coefficient of
x
(not
x
2
) by 2, and then square that.
So for
x
2
−
24
x
, dividing
−
24
by
2
gets us
−
12
.
Squaring
−
12
gets us
144
,
So
c
=
144
.
In general:
Consider the factoring identity
(
x
−
a
)
2
=
x
2
−
2
a
x
+
a
2
If we only have the middle term,
−
2
a
x
, then dividing the middle term by
2
x
gets us
−
2
a
x
2
x
=
−
a
(If we only take the coefficient on
x
, we do not have to divide by
x
.)
Then if we square that, we get
(
−
a
)
2
=
a
2
So as you can see, taking the coefficient on
x
, dividing it by
2
, and then squaring it will get us the magic constant that lets us complete the square.
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